Welcome to the forum mate
Have you read our
PSX Forum Rules 
1.
What is needed to backup PS2 games?
The following sites have lots of info that you are after:
PSXPAUL.CJB.NET
PS2 PLACE (Home of the PS2 newbie bible)
PSXCOPYWORLD (original and IMO still the best )
2.
mod chip
Technically you can boot up a backed up PS2 game on your PS2 console without a modchip, but beware doing this will soon knacker your machine and leave you needing to go out and replace it. I would recommend purchasing and installing a Messiah 2 modchip for direct booting of your personal backups.
Hope that this answers your questions