Hi Luke,
It sounds like you may want to work with someone who’s familiar and comfortable working with files on a server and importing and exporting databases. To answer your questions specifically, though:
1) If you copy the site files and database to a new server (or another place on the same server), then all the files would copy over. The idea here is to copy everything and create an exact copy. So if you did that, everything would copy over.
2) You would use a utility like PHPMySQL that would give you the tools to export your database and import its data to a new database. You’ll want to check with your host to see specifically what tools they provide to allow you to do this.
But again, if you’re not comfortable doing this, I would highly recommend working with a professional here.