PSPs which are able to run homebrew could use a port of "BOCHS" to run basic operating systems on them. However a PSP is far too slow to run any operating systems at useable speeds. PS2s can run linux, if you buy one of the old kits and a USB keyboard, but again it would be slow. PS3s could do this much faster, a Google for "linux on PS3" would help you.
No the PSP can not play PS2 games
No a PS2 can not play PSP games
The PSP is designed to be connected to the PS3 not the PS2
No the PSP was designed to work with the PS3 not the PS2
No a PS2 is worth much less than a PSP
Yes you can i played mlb 10 the show from my psp to my ps2
it is for psp,ps2,wii,360
No, a psp game cannot be played with a ps2.
You don't PSP Go does not play a PS2 game
The PSP and the PS2 do not work together they they were designed for with the PS3
Your thinking about the PS3 not the PS2. The PS2 can not connect with the PSP as they don't work together
ps2 is nice but psp has more features,and a psp is a portable ps3 (but not same grafics) and and we all know ps3 is better than ps2 so I think psp is better.