Why "ne" about bunnies? Shouldn't it be "he"? Or it only works with humans?
No to the second question and yes to the third one, with the exception that some pet owners may refer to their pets with hän/he.
"He" is the plural form (for people). Animals and inanimate plural things like rocks, books, trees ... are referred using "ne".
People are also referred to with "se/ne" quite commonly, though mainly in colloquial registers.