So, im just wondering if when we defeat the opposing faction, do we get to keep their fortress aswell? or will this become a training area of sorts? or does some non-debatable thing happen to the opposing fort that makes you unable to live in it? maybe this will give bethesda last minute ideas or just get some info on the fort's ability for housing after that main DLC quest from them. I also hope i didnt answer my own question here and someone knows more of this than me.

I think that's a reasonable question to be honest. My bet is that the opposing factions' castle gets destroyed or the enemies just stop respawning.
But I think it would be amazing if you could keep the opposing castle as your own, kind of like a trophy of victory haha.

Or if the Dawnguard defeat the vampires they 'cleanse' Castle Harkon and if the vampires defeat the Dawnguard they 'corrupt' Castle Dawnguard.

It's called castle Volkihar. Spelling? Whatever, it's named after the vampires that pull people through ice

Is it? I heard it was named after the vampire leader. We'll settle this... A Bozzer? I guess... never forgets

It was in the Gameinformer leak.