Hi there, welcome to our forum
I don't know really much about PS2 game copying, but I do know that most PS2s can work fine with backupped games on -R media. The thing is however, that the PS2 needs to be modded with a so-called modchip. Without this neat piece of hardware, it's impossible to use backupped games on a PS2.
About the copying of DVD's over 4,28Gb: this is normal. There are techniques however, to circumvent this problem. The most popular technique, is a combination of removing "usesell" parts of a DVD, combined with transcoding the movie.
There are lots of way to do this (a very popular way is with DVD Decrypter (reading), DVD2ONE or DVDShrink (processing) and Nero (writing)). I want to advice you to read the guide about transcoding & backupping a movie with AnyDVD/CloneDCD, in our transcoding guides form.
Here's a direct link to the thread.
If you got any questions, don't hestitate to ask (or use our wonderful search :))