You also forgot to mention playing PS2 games on ps4 using remote play on vita.
But i really don't think a raw ps2 game is possible on psvita. I remember back in school when people had rumors of psp games playing ps2 games, sadly that was all fake, no way could final fantasy X run on that portable hardware that is somewhat of a watered down ps2 that mid tier between ps1 and ps2. To be totally honest, the way a ps2 game could be played is if is remade to work on it, a direct port was never in mind to emulate the system on mobile so it was never considered possible at a functional presentation.
Of course i did mention playing a ps2 game on ps4 using remote play on vita, which i done. If your wifi is actually good enough, you can do it, surprise it works well, something to do in the bathroom or away from the console.
For some people if you have the vita tv and both are wired to same network, it should least be close enough to the experience to say "This works for me" but i not tried it, i had wanted a ps4 slim or pro for the 5GHZ wifi since i cannot use wired connections in my set up. Still reminded that vita is stuck on 2.4GHZ and hope future mobile consoles upgrade it desperatly. O_O
Anyway, I doubt it be possible, but then if the doubting people are proven wrong, is all the more better to be surprised with.