The word ‘who’ functions as a subject pronoun. This means that whenever it is used in a sentence, it must appear before a verb.
Who’s is used when the main verb is BE or HAVE, or in the progressive form (ING). Who’s is the contracted form of ‘who is’ or ‘who has’.
That is the girl who’s (who is) singing.
The girl who’s (who is) in the bedroom is the girl who’s (who is) singing.
That is the girl who’s (who has) been singing since she was 2 years old.
Who’s (who is) that man?
Who's (who has) been smoking in the house?
Whose is a possessive adjective. This means that it will always appear before a noun.
1. There is the man. His wallet was stolen.
(We can change the possessive ‘his wallet’ to the possessive ‘whose wallet’ to make one sentence.)
There is the man whose wallet was stolen.
2. I know a girl. Her father works at the hospital..
(We can change the possessive ‘Her father’ to the possessive ‘whose father’ to make one sentence)
I know a girl whose father works at the hospital.
3. Whose wallet was stolen?
4. Whose father works at the hospital?
A good way to figure out whether to use who's or whose is by trying to make 'who is' fit in your question or sentence. If it makes sense, then use it. If not, please use 'whose'.
Test yourself. See if you can tell the difference between WHO'S and WHOSE at Fun Trivia.