Hello Esther, In terms of the conventional use of English – although one 'can' live in a room, you would normally live in a house, home, apartment, flat etc. and 'sleep' in a room. That aside, let's look at the sentences: "This is the room where I live" [Correct, but the above explanation applies. You would normally use 'where' in terms of a place or a town.] "This is the room where I live in" [Incorrect. The use of 'where' means that the 'in' at the end of the sentence is not required. But you could say 'This is the room I live in'.] "This is the room in which I live" [Correct.] "This is the room that I live in" [Correct.] Hope this helps :)

I think that all four sentences are grammatically correct BUT all of them are awkward. The easy way to express this idea is "I live in this room".

yes, it's a correct sentence

yes, it's a correct sentence

yes, it's a correct sentence