C2 errors in a PS2 game shouldnt be happening, get the disc resurfaced as it's likely damaged. Either that or double check that they're actually C2 errors you're seeing and not EDC or something.
Katamari Damacy has a known issue with one print run of the game, check the redump page for the game here for details. It's almost certainly the cause of your issue here.
As for God of War II, I have no idea why you're having a problem there, there's nothing particularly remarkable about it other than the fact that it's a DVD-9 instead of a DVD-5 like most PS2 games. Make sure the disc isn't warped or damaged in some other way.
Doesn't matter if they work in your PS2, as you would need to run through the entire game and try to experience literally every piece of it in order to figure out where your issues are. Just because it boots doesn't mean it's 100% good. The inverse can also be true, I have a disc that reads fine when dumping due to better error correction on my drive, but I can't even get passed the developers logos and boot the game on console.