bbPress.org

1a. Yes. Just download everything in the bbPress folder (whatever you called it) and then upload that to the new server. That takes care of the file system. Then dump the database and import that on the new host as well.

1b. No, don’t start from scratch, that almost never helps. You can modify what you have going on already.

2. Not sure. There are probably a couple URL related entries you’d have to change, either in bb-config.php or the database somewhere. Not sure what those are exactly, but I doubt it would be too bad.