When choosing between (it’s/ its) and (who’s whose), always read the words containing the apostrophe as two separate words. When you do, the correct usage is obvious.
For example:
1. The dog hurt it’s paw. -Or- 2. The dog hurt its paw.
Read the sentences this way: 1. The dog hurt it is paw. 2. The dog hurt its paw.
Obviously, sentence #2 is correct. "Its" is a possessive pronoun and has no apostrophe.
1. Whose the owner of the BMW in the parking lot? -Or- 2. Who’s the owner of the BMW in the parking lot?
Read the sentences this way:
1. Whose the owner of the BMW in the parking lot? 2. Who is the owner of the BMW in the parking lot?
Obviously, sentence #2 is correct. "Who's" is a contraction for the words "who is."