So I Dm'ed multiple times (probably 13 times? with 2 groups ) and my players seem.... to act enjoyment. Dunno if it's just me being paranoid or seeing the truth of the quality of my campaign. 

Here is where i think i have a problems:

1- I am little bit slow in term of combat, as in it takes me a lot of time to put the initiative order and all.

2- I am unsure on how to prepare with mad players who does the most random things ever.

3- Whenever a story comes in for one of the players the other immediately go on their phones, I am not sure if i am boring them or just not interested in player's background story. Note: I don't know if it's appropriate to ask them to leave their phones on silent or turn them off as they might get phone calls from their families.

4- NPC's, i am by no mean good at making accents. I tried to change my accent few times and even i felt it's not working or feels cringy. 

5- Setting proper amount of enemies. Man... so many times that my players seem to either crush the enemies or it becoming almost slaughter to my players....

6- All of my players avoided clerics and any form of melee classes. We got a Barbarian once who only wanted to try the game but never showed up ever again. 

7- They have the habit of splitting the party a lot almost to a point me having to almost run 2 encounters at once in different places.

Those are all the problems that i can think of right now. Hope i am clear enough and if you can give me some tips i would be more than happy.  I don't want to force anyone to do anything but i feel like that i am losing the grip on DM'ing. 

Hang in there.  There's a lot to learn and juggle as a DM.   A few notes/suggestions to some of your points:

1.(Initiative)  

  a-several places online make encounter sheets that include an initiative tracking section, with numbered slots from 1-25 or so. Here is one example on DMsGuild.  As people roll, just slot them in the right spot.  Then you don't have to reorder them.  There's also a pathfinder wipe-erase version that works for 5e as well

  b-Or, use Matt Mercer's method; have people roll and remember their number.  Then call ask for any numbers about 20, then between 15 and 20, then 10 and 15, etc. This lets you build your list from top down. I moved from method a to method b recently.

  c-some people swear by initiative tents that go over the top of your DM screen.

   d-consider rolling initiative for monsters/npcs ahead of time and noting them down, to speed things up in the moment.

 

2.  This can be tricky, and not something I do easily as well.  It requires the ability to improvise, and not get too stuck in getting the mechanics just right.  

3.  Yes, you can ask your players to put their phones away.  I have a rule at my table that phones/tablets are only to be used for referencing DnD tools or for necessary communication with parents/guardians.  (most of my players are teens).   Many smart phones have an option to silence most calls, but allow calls from "favorites" or "VIPs" to come through.  Maybet his would be an option for your players?  This is something to discuss with your players  (see below)

4.  Then don't worry about accents.  I've shifted to mostly 3rd person narration ("The bartender tells you that Erwin Twinkletoes used to be a regular customer, but hasn't been around for the last week") rather than first person role playing.  I'm too self conscious about my acting ability to consistently do 1st person stuff.

5.  This is hard; there's a lot of swing in 5e combat encounters.  One way to deal with this is to have enemies show up in waves (reinforcements from the next room); you can add/remove waves on the fly without it looking like you are fudging.  Also, it's o.k. for some encounters to be easy and some hard.  Have you tried the new approach to encounter building that's spelled out in Xanathar's?

6.  If you are doing homebrew adventures, you can adapt your adventures to the abilities of their chosen characters.  In many respects, this isn't your problem: they chose the characters they want to play, and if that leaves them poorly set up for melee, that's a consequence of their choice(s).  This is another thing to discuss with them.

7.  I can see how this can be annoying.  But if this is their habit, perhaps you could adapt to it.  Tackle one sub party at once; let the others pull out their phones, or if space allows, let them leave the table for a break; maybe even have an alternative activity that's easy to drop available (for example a puzzle).  Then switch and do the other.

I would encourage you to sit down with your players and talk about some of these things.  Ask how they feel things are going.  What are their goals in playing?  Explain that you are struggling with them going to their phones mid-game.  Ask what aspects of the game they enjoy the most.  What do you most need to enjoy the game?  What do they most need to enjoy the game?  Then begin to make some changes; don't try to change/work on too many things at once.  Then check back in with your players after a few sessions to see how it is going.

 

Splitting the party sucks. This is a really bad habit for the party to get in - it's more work for you, AND it makes it nearly impossible to balance encounters since you don't know whether the encounters' gonna be fought by the whole party or, like half of it. Does that contribute to the difficulty being super-variable? Honestly, that's one thing I'd consider addressing out-of-character. I think it's fine to just talk to them and be like guys, don't split the party, it sucks. 

About players being super-random and doing god knows what... I think that's a common problem for DMs, and it gets worse if a well-meaning DM tries to "set the party back on track". Then the player feels that no matter what random stuff they do, they wind up in the same place, leading them to do even more nonsense. 

As a DM, the way to address that is to focus on what you can control - the rest of the world. If a player does random things, try to figure out - what would happen to the game if they do that? Then narrate the result. Let them face the consequences of whatever the hell they're trying to do. I don't know what 'random stuff' they're trying to do... but don't be afraid to let that have real blowback. Maybe the party gets themselves banned from a city - tough luck, they can't do whatever quest they were going to do there. Or maybe it's in a dungeon, and the guy just made enough noise that the whole dungeon heard - guess they better run the hell away without getting the treasure because all the monsters in the dungeon are coming for them now instead of being spread out. Or hell, maybe the random thing actually works and they get to skip a fight or a dungeon or something. 

That kind of goes for setting proper amount of enemies too. Follow the DMG or Xanathar's rules for difficulty of encounters. If it doesn't come out to 'deadly', feel free to just throw it at the players - it's up to them to figure out how to solve the encounter. Your job as DM is to set out reasonable challenges and then narrate the results of the players trying to solve them - you don't have to ensure they do. 

Quote from Arlong >>

So I Dm'ed multiple times (probably 13 times? with 2 groups ) and my players seem.... to act enjoyment. Dunno if it's just me being paranoid or seeing the truth of the quality of my campaign.[/quote]

Considering whether you can make your game more enjoyable or not is the first step, in my opinion, towards becoming a great DM. The step following that is perseverance; you won't get great if you call it quits before you've given yourself enough time (and in this case, "enough time" means literally just don't stop so long as you feel you can improve in some way even if you aren't sure how to do it - only stop if you literally think you cannot get any better, because that is kind of a self-fulfilling prophecy)

Now to your specific problems:

I am little bit slow in term of combat, as in it takes me a lot of time to put the initiative order and all.

More practice should help. As could a handy game aid, such as this, to help streamline the process. Another way to help this not slow down your DMing flow is to have a player that is willing to take over the tracking of initiative so that you can be doing some other part of encounter set-up or running while they are collecting all the players' rolls and putting them in order.

I am unsure on how to prepare with mad players who does the most random things ever.

My advice is to learn how to react, rather than prepare. Then when a player does something "random" (which in this context really just means something you hadn't thought they would do), you can be in the mindset of sticking reasonable sounding outcomes and obstacles into the game following whatever actions the players end up taking. If you really focus on the skill of improvising, you can run greatly enjoyable campaigns without having to do much preparing at all (it's actually my preferred method, since then I can spend the free time I would otherwise be using to prepare a campaign doing something else like painting miniatures, spending time with my wife other than at the gaming table, or playing some video games).

Whenever a story comes in for one of the players the other immediately go on their phones, I am not sure if i am boring them or just not interested in player's background story. Note: I don't know if it's appropriate to ask them to leave their phones on silent or turn them off as they might get phone calls from their families.

This is a thing I suggest talking over with your players. I say that because they aren't necessarily bored and getting their phones out, but they might be, and that means there are too many variables for any advice other than to speak to them with an open mind and be honest about your own thoughts and feelings. In that way, you can reach a mutual understanding and agreed upon table etiquette - which it is very useful to have be mutual, rather than just invoking your authority as DM to say "No phones at the table", because even without realizing it people can take that sort of decree poorly, and respond to it in a way that makes the problem the decree was supposed to solve actually end up worse than before (i.e. before they seemed distracted because they were on their phone, and after they are not on their phone but are participating in a disruptive fashion because they are, whether aware of it or not, irritated at being disallowed the use of their phone).

NPC's, i am by no mean good at making accents. I tried to change my accent few times and even i felt it's not working or feels cringy.

If it's not enhancing your enjoyment, or someone else's enjoyment at the table, it's a good idea to not spend time or effort on it. If you feel like your game will be better if you get better at doing different voices, maybe find some time away from the table to privately practice until you don't feel the voice(s) come out cringey, while taking a break from using other voices during session time.

Setting proper amount of enemies. Man... so many times that my players seem to either crush the enemies or it becoming almost slaughter to my players

It is nearly impossible to get the exact right feeling of challenge in a single encounter on purpose, and even less possible to get that feeling of challenge from every encounter that happens... at least without those encounters starting to feel like they were all the same to your players.

So what I do, and what you could try and see if you like it, is to focus on providing a variety of encounters on purpose - some that seem like they'll be super-difficulty, some that seem like a cake walk, and a lot that fall somewhere in between. And I say "seem" because what looks one way while you are setting it up can and will go a completely different way once the players are actually playing through it and dice are deciding results - and that's good. Embrace it, and your players will benefit (because the variety is what keeps things fun; it'd be boring if every encounter were a cake walk. It'd be boring if every encounter were almost unbeatable. But you mix enough of each together and every beat down - received or delivered - can be fun).

All of my players avoided clerics and any form of melee classes. We got a Barbarian once who only wanted to try the game but never showed up ever again

I'm not sure what the issue is here... sounds like you are just talking about your players having preferences, and are potentially taking the blame for a player who wasn't really interested realizing they weren't really interested. Doesn't sound like there is anything to "fix."

They have the habit of splitting the party a lot almost to a point me having to almost run 2 encounters at once in different places.

This is a two-part problem. Part 1 being that it puts strain on the DM having to keep track of two different sets of events at the same time, and Part 2 being that it puts strain on all the players involved because they are playing a team game with an arbitrarily incomplete team to help their character and they are reducing everyone's participation time because whichever half of the party is currently being focused on, the other half is not currently participating.

My solution for this is also two part: First, do everything that you can as DM while setting up adventures to make it so that "let's split up, gang" doesn't actually seem like it would help accomplish the goals of the adventure (basically, just make sure you aren't incentivizing or suggesting splitting up in any way with your adventure set ups). Secondly, talk with the players about how splitting the party might sometimes seem like a good thing from a story perspective, but is always a pain for everyone involved from a game-play perspective, and since nothing has to happen in your game unless the players choose for it too, it would be best if the players were choosing not to split the party.

All of my players avoided clerics and any form of melee classes. We got a Barbarian once who only wanted to try the game but never showed up ever again

I'm not sure what the issue is here... sounds like you are just talking about your players having preferences, and are potentially taking the blame for a player who wasn't really interested realizing they weren't really interested. Doesn't sound like there is anything to "fix."

There still isn't anything to "fix". This is another classic case of choices having consequences. If they keep falling rather quickly enough times, it might be enough times that someone dies, gets to roll up a new character, and decides to give cleric a go. Maybe.

It's also possible that they have little to no real idea on what the DnD conception of a cleric (or other classes) is and have only things like WoW for reference where clerics are definitely support only. The only way to 'fix' that is for them to a) read the PHB better, b) watch DnD played on youtube, c) watch other people play DnD.

Some excellent advice above. 

With regards to nobody playing a cleric - there is one person at the table you could persuade - the DM.

NPCs are a great tool for helping to keep players on track, and there are plenty of literary examples when the author wants 'the heroes' to take certain actions without having to explain the whole plot to them: Gandalf,  Allanon,  Belgarath, Elminster, Merlyn.....ok they are mostly wizardly, but the reason for that is a fighter can always fight, but wizards (and clerics) have strange and mystical ways, they have to conserve power for strange and mystical things...leaving the hapless hobbits, half-elves, and barely teenage wannabe-heroes to shine. Or fail dismally.

Run a cleric. Perhaps an absent minded one (Iskaral Pust, if you want an obscure one) to explain his inability to remember to hit every round or cast his most effective spells (You as DM already have a lot to remember, so you are bound to be ineffective here - but make it look like you are doing it on purpose and your players should lap it up!)

Hopefully a side effect will be that somebody will see how hopeless your cleric is, but also see the possibility of what he could be...and will try to show you how to do it better. Boom - a convert to the church!  The trick is in getting the balance right.

But that is the trick to everything when it comes to DMing.

 

If your players keep coming back, and haven't organised a coup, you must be doing something right.

 

 

I have a player keep track of initiative. That helps both with speeding things up for me, and getting the party more into it (they'll always be looking at who's going next- it's a bit less realism but I am willing to trade that realism for enjoyment and engagement)