1. You will need a mod chip in order to boot your backed up games. These can be external usb mods, internal no-solder mods, or internal solder mods. The internal solder mods vvary also, from the crappy neo2/neo4 chips to the daddy of them all
the messiah.
2. Legally you are allowed to back up original games that you personally own.
3. PS2 games come either as cd format or dvd format. The cd's are typically around 650mbs in size. The dvd's can be anything up to 4.7 gigs in size.
4. Tutorials on exactly what burning software/methods you should use can be found at
www.psxcopyworld.co.uk
5. You will need either a dvd-writer to copy dvd/cd games or a cd-writer to copy cd only. Best choice is to go for a dvd writer - Pioneer A03/A04.
Hope this is a useful start to you. These forums have loads of useful information, the search function is ideal for beginners/newbies as you will 99% of the time find the answer you are looking for.