Copying most PS2 games isn't a problem, playing them back is, as you need a modified PS2 to play non-original game discs. The console recognizes the copy by checking a certain part of the disc that can not be accessed by CD writers, only in the factory when the original CD is made. So, in order to play copies which are not complete copies, you must modify the PS2 to stop it from checking the disc. That is done by installing the "mod-chip" into it. There are few versions, but all of them require the PS2 to be pulled apart (probably 30-odd small screws...) and this small "mod-chip" soldered into the circuit boards. The ones I've seen have between 16 and 30 fine wires which must be soldered to certain parts of the PS2 circuits, and it's not an easy job.
As for playing the backup on the PC, I'm not sure how far the emulators got. I know there are few around for PS1, but I don't know about PS2 and if they will play copies.
Any clearer now?