That is called breeding, not taming. You can do the exactly same thing with sheep and pigs and cows and chickens.
Taming is like when you tame wolves or ocelots so they follow you around without you holding the breeding item, can be made to sit so they don't follow everywhere, and teleports to you when too far away.
No, you cannot. They used to be tameable but they changed them to be farm animals only.
Can you make them sit?
Taming is like when you tame wolves or ocelots so they follow you around without you holding the breeding item, can be made to sit so they don't follow everywhere, and teleports to you when too far away.
Rabbits can be bred, not tamed