I don't know about question 1 I'm afraid, but for 2, you'll need to change your Board URL setting (http://example.com/forum), and your cookie path (/forum/), then, if you need to, move the files on your server to wherever they need to go.
Old links posted in threads would then not work, however, so you may want to set up a 301 redirect in your htaccess file.
Old links posted in threads would then not work, however, so you may want to set up a 301 redirect in your htaccess file.