how to copy already ps2 back-up???

Good media is best - like your Verbatims. Actually I use cheap PC World CDs in the tub. Anyway, if you're buying a CD writer, do two things: 1) Go to www.goldenhawk.com for a list of writers compatible with CDR-WIN b) go to www.elby.de/CloneCD/english/ for a list of writers compatible with CloneCD.
Then buy a writer that's compatible with both nearest to the size of your wallet. These two programs are the "must" for PS2 backups as a search through this forum will confirm.

Good luck