"Чей" should agree in number/gender/case anyway.
Actually both groups of questions above are correct, but they have slightly different meanings.
Чья это комната? "Whose room is this?" - here "это"="this" does not really modify noun "room", but refer to some undefined object. "Whose room is this object?"
Чья эта комната? "Whose is this room?" - here "эта"="this" does modify noun "room" and agrees with it.
The first way is more common though.