In general yes, but it depends on your burner. If your PS2 is an older model (V4 and under) then you NEED to use DVD-R, the drive is incapable of reading +R at all. If it's a late V4 then +R is ok. V5 and up are good with +R. And lastly, if your burner is better at burning +R, then by all means use +R.
Does it matter which speed I burn the games at?
Everyone will tell you it does, but it hasn't in years. Back when burners were only 8x (CD), you needed to burn at 1x (CD) to get solid results with PSX games. Nowadays? Just don't do it at full speed. 12x for CD's, 4x for DVD's. The important thing is giving the laser adequate time to make a good burn, but too slow is bad as well now.
I've noticed on newsgroups and bittorrent that a lot of the games are less than 700mb. Does this mean they are ripped or are a lot of PS2 games just CD games?
Either or. If the game is under 700MB for the most part it's a CD game. But oftentimes it's a compressed DVD game. Most of the games from Nippon Ichi, for example (Disgaea, La Pucelle Tactics, Phantom Brave) compress nicely to 600MB or so, but are actually 2GB games! But yes, a LOT of PS2 games, to date, have been CD games. Crash 3 was a CD game. It takes about 5 minutes to load because it decompresses everything. They SHOULD have just put it on a DVD, but they didn't. Bleh.
When burning DVD films it can be an arse because they can be dual layered. Are there any dual layered games for the PS2 and if so how would you burn them?
One or two. Gran Turismo 4 is the only one you're likely to run into. There are rip-packs on the web which will allow you to burn it as two discs or one disc with some compressed video.
Can the PS2 read CD-RW, DVD-RW or DVD+RW?
Probably, not usually, and hahahaha no. In that order.
Bear in mind that Sony has put the world's SHITTIEST lasers in the PS2. If your unit is V1-V3, it's debatable whether or not you'll EVER get your backups to work.
Oh, and you are aware you need a MOD chip, yeah?