The extensive use of plastic bottles, which can take many years to biodegrade, is an environmental hazard in it’s own right.

Correct sentence: The extensive use of plastic bottles, which can take many years to biodegrade, is an environmental hazard in its own right.

In this case, the contraction "it’s" is inappropriate. If used, the reader would be confused as to what the "right" referred to.

We decided that our contribution to the game would be attacking and that they’re contribution would be defending.

Correct sentence: We decided that our contribution to the game would be attacking and that their contribution would be defending.

The possessive determiner "their" lets the reader know whose contribution would be defending. In this case, it is some group of people. "They’re" is a contraction of "they are" and is inappropriate and illogical to use.

The celebrity actress who judged the beauty contest found it difficult to decide who’s answers were better.

Correct sentence: The celebrity actress who judged the beauty contest found it difficult to decide whose answers were better.

"Who’s" is a contraction of "who is" and is not appropriate to use here. The possessive determiner "whose" is grammatically correct for this sentence.