To play back up DVD's (that you own of course...), you first need to check what version of ps2 you have....
version 1 = starts with "U1" and has 10 case screws.
version 2 = starts with "U0" and has 10 case screws.
version 3 = starts with "U2" and has 10 case screws.
version 4 = starts with 'U3' 'U4' 'U5' or a 'U6' and has a total of 8 case screws.
version 5 = contains the letter 'R' at the end (example SCPH-30001 R).
version 7 = 3900X is the new PS2 Version 7
once you know this, you then have to use the right media (DVD-R/DVD-RW/DVD+R/DVD+RW) as the different versions only work with certain media.
Version 1 - DVD-RW
Version 2 - DVD-R and DVD-RW
Version 3 + 4 - DVD-R
Version 5 + 7 - DVD-R, DVD-RW, DVD+R and DVD+RW
I have a version 5 and use Mirror DVD+R (good quality yet cheap, check www.kelkoo.co.uk for prices) and i burn them using Nero 6 (can get this off kazaa)
not sure why it's playing some DVD's in black and white. The only reason i can think of is if the DVD's are in NTSC format - in which case you'll need a NTSC combatible TV or a NTSC - PAL convertor (�40 - �60).
As for back-up games, you'll need to either chip your ps2 (voids warranty and is v. tricky) or get a flip top lid and swap magic. the best programs to use are clonyxxl and then clonecd. when making back ups check the back of the box to see if the game is written on a DVD or CD.
hope this is some help - still unsure let me know.