Since the season 8, the Winchesters are living in a new house, a 'hunter' house. How did they get it? Who owns it? What is it for?

I assume you are talking about the bunker. They discover it in 8x13. They meet their grandfather Henry Winchester, who is a proclaimed men of letters in the episode before. The short story is, the men of letters are known as a group of knowledge keepers, who carry and pass on a vast amount of information about the supernatural creatures and how to kill them. They occasionally helped hunters out back in the day.

Sam and Dean get a key to the men of letters bunker and in 8x13 they find it and eventually make it their tahanan base. It is full of many goodies including: bedrooms, store rooms, archive rooms, torture rooms, dungeons, firing range, libraries and probably much more.

It is full of information, so its in some sense a aklatan for researching lore. And like I said, it is their tahanan base, and it is warded to keep demons and mga kerubin from finding it. Dean sees it as the first real tahanan they've had since childhood. And since Sam and Dean are 'legacies' of the men of letters (and there aren't any alive today), I guess they own it then.

I don't think we're supposed to think about where they live... because they kinda just live in so many different places and it's pretty random, so you probably shouldn't think too much about it ;)