Good questions!
Firstly, if you use the forum's bread crumb trails (those things at the top of the forum window that says what forum and thread you're in - like the photo below)

instead of using your browser's back button after reading a post that you don't reply to, the software should automatically mark the post as "read" (thus, there will be now "new" icon next to it, and the forum folder will turn grey.) If that doesn't work, then there is a link at the bottom of EACH forum that says "Mark Forum as Read". If you click that, it should remove all the "new" icons next to each thread that has already been read.

As for the moving of the old threads, currently there's no way to do that, but maybe with the new website software, maybe something along those lines is possible.