1. As Roman reminded us, perhaps the most natural question would be: "Who does it belong to?"
2. "Whom does it belong to?" would be grammatically correct, but notice how much energy is needed to pronounce "whom."
2. "To whom does it belong?" might actually be the most correct of all, but it would be much too formal. I do not think that most people would speak that way.
Who do you live with?
Whom do you live with?
With whom do you live?
P.S. This is only my OPINION: If you are doing any formal writing (for example, university reports), I think that you should use "whom" when it is grammatically needed. In ordinary conversation, it is better to incorrectly use "who" -- because you do not want your friends to think that you are strange! (I always use "whom" in speech and writing because I am an old man, so I do not care if people think that I am strange.)