Hi,
"Questions: Where can I go to learn what it means to "backup" my course
to my own PC, to get a copy of Moodle "running" on it (I assume this
can be done offline); how to back it up, upload, and restore. "
First, you need to have a copy of moodle running on your PC. This depends on what Operating System you are using. If you are running Linux, you can use the Apache, PHP and MySQL programs to get it running. Instructions are on the the download page and here
If you are using Windows XP, you can also install it following the instructions on this page. There also seems to be a one-click development in progress.