Hi brentazzzz and welcome to CDF,
I’m not sure if copying PS2 with with DVDFab works. But anyway, you need to modify the PS2 to make it possible to to play the game backups.
The best and most difficult way is to install a modchip in your PS2 but they are hard to find these days (at least here in Europe). Another way, which doesn’t require a hardware modification is the so called swap magic disc.
Regarding the copy software I can tell you that DVDDecrypter is the ultimate thing but you can also create your backups by simply copying the games with Nero.