well it all depends on when u bought your PS2
some of the early ps2's can't play certain DVD movies (mostly bootleg or others)

u may need to update the dvd drivers on your PS2, u can obtain the new drivers if u buy PS2 DVD remote.

That will update the drivers, but it requires at least 3MBs of space on our memory card.

if u have the new PS2's(Model # 30001R) u can just flash the BIOS with the disk an not use ur memory card.

an to answer ur last question some of the first generation (95-96) PS1 games wil not work on your PS2. There is a list of PS1 games that Sony has on there site but i lost the link...
"if murder makes me richer than i'll be a killer"