Do I have to tame animals like sheep and pigs In Minecraft?

Ok so the main question is only part of what I ask. So I play on a survival server with other people and One day a Zombie Pigman comes out of my nether portal so I decide to fence him and keep him as a pet. He is there for a while and then I go off and pause the game for a second and come back and he's gone! The same thing happened with my chicken that I kept in my house for a short while until it disappeared too. Is there something I have to tame animals with? (not including the zombie pigman) and how can they be tamed if so.

Different animals in minecraft are tamed using different objects but the main similarity throughout is that you must right click on it with said item. (This is off the top of my head but I'll try and make a list of what to use)

'Love' mode (will follow you when holding said item)
Pig-carrot
Cow-wheat
Sheep-wheat
Chicken-seeds

Actual taming
Ocelot-raw fish, hold shift and walk towards it slowly, don't look directly in the eye and make no sudden movements. When it stops in front of you right click.
Wolf-bone, simply right click
Horse- keep right clicking on it with nothing in your inventory and you should get on its back, after a few tries and being bucked off a bit, you should be able to remain on for as long as you want and little heart particles will come off the horse (as with all animals when tamed) then just click e while riding and put a saddle into the slot next to it in your inventory.

Well, that'd proboably be a server problem, considering how chickens aren't supposed to despawn. Zombie Pigmen will, but I believe if you attach a lead to them and something they won't (Not sure, haven't played in a while). Might be a griefer, may be a glitch. Just try and save up eggs to rid yourself of this problem.

This is a result of despawning. Some animals you can tame, others no. The three animals in the game (So far) that you can tame are wolves, horses, and ocelots. Wolves are tame by continuously right-clicking the wolf with bones in your hand. Sometimes you will need one bone, other times, you'll need 7. Ocelots are tamed with raw fish, but in a different way. Crouch with a few raw fish in your hand and WHILE crouching, walk up to the ocelot. Once you get close, right-click the ocelot with the raw fish. You'll need 1-3 raw fish to do this, but it takes patience! Ocelots often run away. Horses are tamed by continuously riding them using right-click. It WILL throw you off the first 10 or so times, however, until you tame it. To make it easier to tame, feed it apples, golden apples, or enchanted golden apples. Once it's tamed, you can only control it when you put a saddle on it. You find saddles in chests in dungeons. You can right-click the horse with a saddle to put it on or you can ride the horse and press 'E' on your keyboard and equip it. You can also boost horses' armor stats using horse armor. There's gold, iron, and diamond horse armor. It is NOT craftable so again, you must find in in dungeon chests. You equip horse armor like you do a saddle. In the 1.6 or 1.7 update, you MUST have water within a certain radius of animals to keep them from despawning. This does NOT apply to your zombie pigman. But, you CAN use a name tag, again found in dungeon chests to name your pigman, or ANY mob you don't want to despawn. To name them, rename your name tag in an anvil, then right-click your zombie pigman or any other mob or animal. Hope this helps!