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

Also since the psp had only one analog stick, for PSP games like Monster Hunter(and the like), where they used the PSPs face buttons as a analog stick replacement - 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 to conform to the new system?