yes, except for squids and wolves.
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Use wheat which you can harvest/steal from villages
You must use wheat. Hold it in your hand.
Yes. If you are holding wheat in front of a sheep and it's looking at you it will start following you. It will even follow you into lava.
If you hold wheat in your hand, all passive mobs, including pigs, will come towards you.
Wait until 1.9 when you can lure animals to where you want them to go using wheat. Pre-1.9 though, it can be quite challenging.