Now you are armed with the vital piece of info you should find plenty of info to answer your questions. If you still have specific queries that aren't answered, please post back. Actually post back and let us know how you go regardless! :)

If you don't want to do that then you can do a local backup on your AWS server then copy that to your local server (sftp or rsync or however?). Then restore your backup to your server.

I linked to the TKLBAM docs in my post above (and again here).

The Example usage scenario is going the opposite way to how you're doing it but the theory remains the same. If you want more info about the specific commands then have a look at the Manual pages.