It's a while since I marked a thread as solved, but I think I recall that you can go to the first post in the thread, edit it and mark it as resolved. But from memory, that option expires.
I wouldn't sweat it too much - probably about 1% of posters here mark their threads as resolved.
As for thanks, I think it says in the pop up, something about how you should only use it for posts where alot of thought or effort went into it.
Again, it's up to you. I'm not sure that anybody really pays much attention to that stuff either.