"Whose car is that?"
Translation:Kies aŭto estas tiu?
Not sure but I though that if it is a know thing ("i know about the car, and I ask whose is it") then it's "kiu". If it's "what kind of thing is that" kind of question, then it's "tio". And people always qualify for "tiu" because we already know it's a person so we are asking who that speciic person is. Something like that. But again, not sure
Tie, ties and tiu are all entirely different words:
- tie means "there" (-e concerns location);
- ties means "that one's" (-es concerns possession);
- tiu means "that one" (-u concerns a specific referent).
In this sentence, the speaker is referring to a specific car (tiu aŭto) and asking whose (kies aŭto) it is.
Your sentence would mean "Whose car is there?", which has an entirely different meaning.
As to your question in general: they do not necessarily agree, even if both refer to the same referent. Both words fulfil their own separate function in a sentence. The English sentence "I see the one who loves me" would translate as "Mi vidas tiun, kiu amas min". In the first sentence you see her (object, accusative), in the second sentence she (subject, nominative) loves you.