Do I have to back up the photos and videos on my phone before trying to restore it?
Do I have to back up all the photos and videos on my 4GS before trying to restore it on itunes?
You should be backing up all your photos and videos at all times. Backups are not just for restores. The iPhone is a very insecure place to store the sole copy of anything you feel is important: hardware failure, loss, theft....