As Denniss said, you should not need a driver for an optical device. If the Device Manager says it's there and has no exclamation marks over it, it is installed properly.
I've encountered the issue about it not showing in the File Explorer. If my memory serves me, it will show once you put a disk in.
To answer #1: The driver update sites and programs are very untrustworthy. Only download drivers from the manufacturer's site.
#2 & 3: For installing an external drive is just as fine as an internal. If a game constantly loads video clips etc. during playing the game, USB2 may be too slow, USB3 should be fast enough even for that.