There are some PSP ports of PS2 games so that's something at least for him.Won't be possible.
Vita isn't powerful enough to run PS2 games at a playable speed.
Hope is not lost completely lost though, I remember reading that it would be possible to play Dreamcast games at full speed on the Vita.
What do you mean? Ps2 emulation isn't bad on computers. I doubt the Vita would be able to emulate a PS2 at playable speeds but the way phones keeping evolving I wouldn't be surprised if we see an emulator on Android like we have Dolphin.Given how bad the overhead on PS2 emulation is on PC, I doubt there's a way portable devices can emulate a PS2 any time soon.