I'm confused because I don't know the differences between which and that when I talk about object of an object. Furthermore, I don't know how to use the relative clause correctly when I talk about object of an object. Is this sentence correct? - The house that/which TV was damaged in the fire is now fixed.
You would use whose. Whose can be essential or not, depending on whether the information is important. It is used for both people and things, even though it sounds a bit weird when it isn't referring to people. Trust me, it's OK to use it for things.
The house, whose TV was damaged in the fire, is now fixed.
The house whose TV was damaged in the fire is now fixed.