TG = Thieves Guild of course.

Can you?

Can I?

Raze it to the ground. There, no debt anymore.

You mean like in Oblivion? I dont think so. But there is a perk that allows you to bribe the guards.

I can't find where to do this if you can. I heard a character in game say something about this, but the guy at the winterhold college also says he'll enchant stuff for you, and he doesn't.

I don't think so, I think its taken care of with the guards in the hold, you pay them half when they catch you, you add more holds to the TG in the questline, but you need the perk for all the holds