Player's Handbook, page 305

Is it possible to have a crocodile as a companion? I would love to have a crocodile fight alongside with my character, preferably a ranger or some sort. If so, please let me know if there is any info from any book that explains it.

Take a look at the beastmaster subclass. Makes sure to take some UA to make it not the worst subclass avaliable.

Can my druid turn into this at level 5 after meeting one in the adventure?

If you tell this to your DM at the beginning, S/he can put a crocodile as your companion like an ordinary PC and change the CR of the game for this.

Berkaykarsli
You are making a lot of assumptions
Like that just because you ask for a crocodile that means that you, regardless of class/subclass will get one
Also the wording suggests you think they HAVE to.
You are incorrect.
You can ASK (not TELL) you DM if they might consider it. But they are fully within their rights to say no, In fact they would be showing favouritism if they let you have one

Come on, crocodiles are more dangerous than this

Armor class is too low. Should be at least 13

Crocodile

Give them the ability to go into a death roll and be able to twist off limbs! then you have a scary little beast to throw at your players

Crocodile's have the strongest bites ever recorded, absolutely dwarfing lions, tigers and even jaguars which have the strongest bite of any bit cat, these creatures are way too weak to be considered crocodiles.

Shouldn’t the escape DC be a lot higher? Getting out of a death roll grapple is near impossible for humans, and with this DC a cow (comparable in size and strength to a water buffalo) would have a 65% chance to escape. In the wild that looks more like 5-10%. Crocodiles have survived millions of years of evolution for a reason.

should have a death roll ability.

Best way would be to see if any of your players have some kind of speak with animal or animal friendship spells if you want to tame one. Otherwise **** it man it's a fantasy game, it's all made up anyways just give your ranger a crocodile and you role iniative for it etc. If the ranger controls it's actions and you control the outcomes, eg. Ranger: I command Fluffy to bite the guy! You, rolling for Fluffy the croc: okay he hits and does x damage. etc.

I think this would be way fun!

up to the DM.  You could probably homebrew it.

yes

it is 1/2 cr and so it meets the requirements

Yeah

I think so, if my memory serves correctly at lv 4 you can wild shape into a monster with a combat rating of 1/2, so yes.

At level 6 a normal druid can become a CR 1/2 creature (Like a crocodile) unless you took circle of the moon which allows you to go up to CR 1 at level 2

NVM, it's level 4 not 6, so yes