No only Small cats named Ocelots
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Nope. Just horses, unicorns, nightmare horses, pegasi,, cats, big cats and ostriches. lol
You get cats by taming Ocelots with raw fish.
You can only tame wolvesand cats in original Minecraft by giving them a bone from skeletons and right clicking them, they can have any number of bones. But, if you get a mod you could tame Chickens, Cows, or maybe pigs and that. Its best to check out the Minecraft Wiki. Even other mods like Mo' creatures, adds creatures and lets you tame them, like horses, cats, goats, big-cats and such.
Yes
No, Creepers just flee from them.