How do PS1 and/or PSP games look on the Vita? Do they fill the screen?

Also,for PSP games like Monster Hunter, where they used the face buttons instead of a econd analog stick on  instead of a second right analog, they substituted the face buttons - if I play them on the Vita, can I use the second analog stick? Or do I have to use the face buttons? 

Will the games play the same as they did on the older system? Or will there be changes?