Hi, new to D&D and unsure about how well familiars should behave when given instructions. 2 main things.

1) I understand that the find familiar spell says "Your familiar acts independently of you, but it always obeys your commands. " but that an imp familiar from the Warlock Pact of the chain says: "An imp will proudly serve an evil master of any kind, but it can’t be relied on to carry out tasks with any speed or efficiency."

If feel there might be a conflict between these. For example I asked my familiar to watch over me and wake up me up if anyone tried to mess me me/hurt me. We had 2 players on guard duty also. At least 1 or 2 other the team are untrustworthy and we're fighting through an orc infested area so it's not exactly safe. The DM had my imp leave the room because it spoke to the players and heard an odd wind sound from the next room. They didn't try to persuade/trick it, it just decided to go have a look. I don't want to 2nd guess my DM but it leaving the room seems like it's disobeying orders? It's only like a short time so does that count as being inefficient?

Another time I asked to it follow 2 players and protect a specific 1. The player that the imp wouldn't care about was about to be attacked and the imp decided to attack the creature before it reached him. It feels like a very pro-active action for the imp. Considering how it behaved previously this seems like it's doing the opposite. I would of assumed it would of done nothing to help them until it's orders to protect the specific character kicked in?

From the D&D info I'd read I feel like the imp would be in danger of only literally obeying orders (like the letter of the orders but not the spirit) providing it doesn't put its master in danger. I'd never ask it to cook as I'd be worried of it over/under cooking food (so it's unpleasant but no harmful) or spend too long making it. So the more complex the task the iffier it would be the imp would do it correctly. I was expecting to control the character myself (if not always then at least whilst it was within range of me being able to talk to it either via speech or telepathy). I guess that's a mistake on my part with not checking how the DM would run things. 

Having a familiar that "might" disobey instructions feels like a nerf, making it much less useful when that can put my character in danger.

2) Another thing that I'm not 100% sure on is the whole telepathic bond.
"The imp can enter into a contract to serve another creature as a familiar, forming a telepathic bond with its willing master. While the two are bonded, the master can sense what the imp senses as long as they are within 1 mile of each other."

but then in the more general familiar spell it says:

"While your familiar is within 100 feet of you, you can communicate with it telepathically." Would I be right in thinking within 100 feet you and the familiar can talk but 101 feet to a mile it's more a vague sense, maybe like emotions?

Happy to hear any thoughts on this.

So it sounds like your DM is running the familiar as if it was another NPC, and based on my experiences in DnD, that's not a thing I've ever heard of happening. Every time I've seen or heard of someone using Find Familiar, the familiar often acts more like a drone than anything else. It moves exactly where ordered, does what it's told and has no will of it's own.

The reason for this is you aren't even summoning an imp. Read the first line of the spell and see how it mentions that what you summon is a spirit that takes on the form of a creature. So what you are really doing is summoning a spirit (which is vague and world dependent on what "spirit" means), and just shaping it into the form of an imp. You could even make it be a celestial or fey instead of a fiend, and then later on turn it into an octopus. It sounds like the people are treating the imp as an actual imp, instead of what it really is which is a spirit given a body.

Ask your DM if the personality would change if you gave it a different form, like a celestial rat. If so, ask them in advance what those personalities are so that you can actually understand how your spell is supposed to work without the confusion.

Yes, your familiar is being slightly nerfed.  A familiar summoned through the Find Familiar spell is a spirit that takes the form of a creature of your choice.  It gets the features and abilities of that creature, but not the personality.  So you can ignore the bit about Imps being slow and lazy, that applies to the actual creatures and not your spirit familiar.  Your familiar must follow your orders to the best of its ability, so your DM should not be doing anything that contradicts that.

You should also ignore the Familiar Variant versions of creatures.  Those exist for people who want to adopt a creature that they meet while travelling, which is not the same as a summoned familiar.  This means you use the telepathy rule from the spell, 100 foot range only.

Quote from Gruntler >>

...  A familiar summoned through the Find Familiar spell is a spirit that takes the form of a creature of your choice.  It gets the features and abilities of that creature, but not the personality.  So you can ignore the bit about Imps being slow and lazy, that applies to the actual creatures and not your spirit familiar.  ...

 
If, by use of the standard spell, a familiar "takes an animal form you choose: bat, cat, crab, frog (toad), hawk, lizard, octopus, owl, poisonous snake, fish (quipper), rat, raven, sea horse, spider, or weasel. [then] the familiar has the statistics of the chosen form, though it is a celestial, fey, or fiend (your choice) instead of a beast.

If your familiar is an imp then it is already a fiend and could, depending on interpretation, remain in it's original form.  FF still says that it "always obeys your commands".  A familiar can be described as a spirit despite being manifest as a physical form and adopting the stats of that form with some buffs.  People might potentially be described as souls.  Not sure how different a familiar imp and an unfamiliar imp might be.

It sounds like your DM wants to play the imp as an npc and, if anything, that might be something you could play to your advantage.  Play into and raise the issue that "An imp will proudly serve an evil master of any kind".  Perhaps talk up your attempts to make it feel proud of it's work.  You might have your own ideas for a relationship dynamic but I imagine a potentially fawning fiend wanting to do its best for you within it's limitations.

Thanks for the responses everyone. Yup, I made the mistake of confusing my spirit familiar with an actual imp (Familiar Variant) and the DM just didn't see the mistake either. This is literally my 1st D&D and it's also the 1st time the DM has been a DM; and not even sure he's played as a Warlock.

I do need to point out the issue as the DM thinks the "imp" gets my soul if I die (and is thus trying to "interpret" my orders making it questionable if it's even doing the job). Having to be extremely specific in my wording atm when I want it to protect me, specifying all the directions I might be attacked from which gets draining when this is for every order. If my familiar is only going to be loosely following orders I don't see an advantage as any task would be done unreliably.

So just to check, the spirit has no will of its own? It's just an extension of myself basically? Does the intelligence of the spirits form come into play much with figuring out the best way to follow an instruction? Or is it just for situations than need a intelligence check/perception?

In every game that I’ve played in the familiar is an extension of the PC and is played by the player. For situations where an ability check is needed use the familiar’s ability score, but other than that they’re controlled completely by the player. 

Quote from Alpharius9 >>

I do need to point out the issue as the DM thinks the "imp" gets my soul if I die (and is thus trying to "interpret" my orders making it questionable if it's even doing the job). 

Umm, that's not how familiars work... a more plausible idea is that the familiar is waiting to drag your soul off to your patron upon your demise, which could be part of your character's story arc.  Then your companions would have to try and recover your lost soul.  ;-)

Having to be extremely specific in my wording atm when I want it to protect me, specifying all the directions I might be attacked from which gets draining when this is for every order. If my familiar is only going to be loosely following orders I don't see an advantage as any task would be done unreliably.

So just to check, the spirit has no will of its own? It's just an extension of myself basically? Does the intelligence of the spirits form come into play much with figuring out the best way to follow an instruction? Or is it just for situations than need a intelligence check/perception?

It should have its own personality to make the game more interesting, but it cannot argue or act against your wishes, it's your personal servant.  Usually the familiar is controlled by the player, but I think that if you're not actively directing the familiar then the DM should be free to inject some harmless behaviours for added flavour.  It's usually better this way as the DM has one less thing to control, letting them focus on the monsters and NPCs and everything else they have to do.

Intelligence is not really an issue in that sense, just use it when an Intelligence check is required.

The spell does say that the familiar does act independently of you. I could see that being interpreted as the DM controlling it, but to be honest, with so much to track with being a DM, I'd kick that back to the player regardless. Maybe for guarding the camp at night, I might take over. if, the last thing I need as a DM during exploration, travel or combat is another creature to track, act out and integrate into the setting. The player can deal with that.

It investigating a sound while having been instructed to guard you is, depending on personality, a valid behaviour. In hearing the sound, it's detecting a potential threat, and therefore investigating it is a valid interpretation of the instructions. Unless you said explicitly to not leave you alone, I think that's valid. The familiar protecting the character, because it didn't contradict your command, could do so due to it being able to act independent of you.

That said, unless both you and the DM are happy and want to do otherwise, the relationship shouldn't be antagonistic. While your instructions should be enough to cover your intent, I don't think the DM should be lawyering it up and trying to find loopholes to make the familiar disobey you. If you wanted that as part of the story, that's one thing, but it shouldn't be imposed. As you've said, it makes for an oppressive game, if it's unwelcome.

Quote from Gruntler>>

Umm, that's not how familiars work... a more plausible idea is that the familiar is waiting to drag your soul off to your patron upon your demise, which could be part of your character's story arc.  Then your companions would have to try and recover your lost soul.  ;-)

It's not really the type of group that would do that sort of thing. More a group working together for mutual gain than we care about another. Several less respectable characters have found loot and hidden it on their person. I'm playing an evil character (changeling warlock) who's pretending to be a hero (hoping to do a cool twist at the end). On the trying to build up trust part with the group atm.
1 of the players stole a chest of gold which me and a rogue released as he's a terrible liar (which being an amazing liar I cud tell straight away). Got the rogue to steal the cash that ranger had taken whilst he was asleep and fairly give it to everyone which made him salty. When he woke up he tried to eat my familiar when it was looking like a small animal. This was why I got it to make sure nothing happened to me at night. Not the type of group I'd expect to rescue my soul lol. 

The idea of if I fail my patron getting my soul taken definitely has appeal though. I'm working for an archfey as seemed closest to what made sense. Since I don't know much about D&D I was using Warhammer knowledge as a guide for character fluff (Tzeentchian patron type)

Quote from Gruntler >>

It should have its own personality to make the game more interesting, but it cannot argue or act against your wishes, it's your personal servant.  Usually the familiar is controlled by the player, but I think that if you're not actively directing the familiar then the DM should be free to inject some harmless behaviours for added flavour.  It's usually better this way as the DM has one less thing to control, letting them focus on the monsters and NPCs and everything else they have to do.

Intelligence is not really an issue in that sense, just use it when an Intelligence check is required.

Ok, so it has a personality which is usually controlled by the player (thus not going to be trying to find loopholes in instructions) to free up the DM. The rest, is just fluff to make the game more natural. 

We're only playing once every 2 weeks so plenty of time to talk to the DM next time he's free to sort all of this. Big help as at the start I was totally confused about this all. Thanks everyone.

RAW, it has a personality, "always obeys your commands" and "will proudly serve an evil master".  If your DM is a 1st timer then it may be unlikely that they've intentionally gone off-script so, like you've said, it may just be a matter of giving a reminder.

one thing to keep in mind is that the warlock getting those enhanced familiars is that you choose whether it is Celestial, Fiend, or Fey you can have a Celestial or Fey Imp there is nothing stopping you from recasting that spell to make your Celestial Imp a Pixie, you can change it every casting of the spell. 

That's amazing.
Having said that, there's also nothing stopping the DM from following the "always obeys your commands" rule.  A fey imp might not be so thematic but, even by its proposal, it might help break the 'chain''. 

You make 2 choices when you cast Find Familiar.

You choose the type of spirit, Celestial, Fey, or Fiend. Up to you if it's the exact same spirit no matter what form it takes. Example, mine is a Celestial spirit of my twin that died at birth.

You choose the form it takes. This is the beasts listed in the spell, or the extras for Pact of the Chain.  Example, that same Celestial twin of mine usually takes the form of an Imp to look very much like my Tiefling's "Mini Me" with wings.

By design, this is your NPC. Not the DM's NPC. Just like the Beastmaster pet, Artificer Steel Defender, etc. It's more than just another NPC, it's an extension of your "character" and a class feature. Taking over this feature is like taking over the Fighter's extra attack, or the Cleric Patron choosing spells for them.

The "Familiar Variant" entry on some monster stat blocks have nothing to do with the Find Familiar spell, or those summoned by it. I'm hoping this clarification gets added to the spell and those entries in the upcoming "refresh". Familiar Variant entries apply to the actual creature (no celestial, get, fiend choice) choosing to be a familiar to anyone. This is how to get a familiar if you don't have access to the spell, any class can do the RP to gain this trust. 

The Familiar Variant version is actually the DM's NPC, though. You meet this one through the DM as part of the adventure. It's like all the other pets, mounts, hirelings, etc. This one just has an extra bonus to it. It has nothing to do with the Find Familiar spell, it just does what is listed.

BUT, the usual caveat of the DM choosing to ignore this. Either through ignorance, story reasons, power monger, etc he might control your NPC from time to time or always.

Quote from Jeramiah >>

The "Familiar Variant" entry on some monster stat blocks have nothing to do with the Find Familiar spell, or those summoned by it.

 This has been stated multiple times in the thread, but people are still quoting the flavor text of the monster, so I want to emphasize this.

A Pact of the Chain warlock familiar is not an Imp (Familiar Variant). They are two different game mechanics. Any familiar gotten through the Find Familiar spell (Pact of the Chain or no) is 100% controllable by the PC, although they are encouraged to roleplay it as a separate entity. The familiar variant monsters are an entirely different mechanic that is explained in the monster stat block.