The correct answers are The alien wagged its three tails happily. and The spaceship is theirs, but the alien is ours.

Its is the correct possessive adjective for a thing or animal. It's with an apostrophe is a contraction for "it is" or "it has," making "it's daily bowl" incorrect.

Theirs and ours are correctly used as possessive pronouns that stand alone. "There spaceship" is incorrect because there refers to a place; the correct possessive adjective is their.