No, that wouldn't make any sense. Don't go too far with the 'belonging/possessing' thing. It's not that every single word which can somehow depict possession takes Genitive.
Firstly, 'ten' is just a determiner, so it has nothing to do with possession.
Secondly, normal possessives (my, your, their, etc.) also don't automatically take Genitive, they take whatever the noun takes. So "Mój pokój jest duży" (My room is big) takes Nominative for 'my room', because it's the subject of the sentence.
Genitive is used when possession would be implied in English by using "of" (a friend of my dad = przyjaciel mojego taty) or by Saxon Genitive (my brother's car = samochód mojego brata).
No, "Kogo jest ten pokój?" is a mistake some Polish speakers make, but it's definitely wrong.
I guess you wanted to say something like "Byłoby to prawidłowo?"... "prawo" is either a form of "right" (as opposite of "left"), or it means "the law".
Also, you can't put a space before a question mark in Polish. I don't know if it's correct in any language other than French.