Question: can ppsspp run ps2 games?
Answer: PS1: No, PPSSPP won't support PS1-PSP games. PS2: No, the PSP was way too slow to ever have a hope of emulating PS2, so PPSSPP won't, either. Nintendo DS: There's a homebrew DS emulator for PSP but it's so slow and beta-esque that it's not worth your time. Also, PSX and PS1 both are and aren't the same console.