The correct answers are That half-eaten pizza is mine! and Please don't touch my chocolate milk.

Mine is a possessive pronoun that stands alone, while my is a possessive adjective that must be followed by a noun (like "chocolate milk").

"Hers sandwich" is incorrect because hers is a pronoun and shouldn't be followed by a noun (it should be "her sandwich"). "Your's" is incorrect because possessive pronouns never use apostrophes; the correct spelling is yours.