Are all PSN PSP games compatible with PS Vita?

No sorry, but Sony have said they are aiming to make as many compatible as possible. Heres a list of all the initially compatible games.

I found this FAQ which answers a few questions but I'm not sure if this is the definate answer you were looking for. It says (about half way down):

Q: Is PS Vita compatible with other PlayStation platform games like PS3, PS2, or PSP? Do you have any plan to support other PlayStation platforms in the future?

A: Users can play PSP titles, minis and PSone classics titles which are offered on PS Store. We do no have any plans to make PS Vita compatible with PS3 or PS2 titles at this point.

Q: Is PS Vita compatible with PSP content other than games such as video and comics available on PlayStation Store?

A: SCE plans to make those content available on PS Vita.

Q: Can PS Vita users continue using their save data for PSP games that they have also downloaded from PlayStation Store to PS Vita?

A: We are looking into the opportunity to do so.

The bolded would suggest no, only confirmed titles would be supported however this is really vague and still doesn't completely prove or disprove that the use unsupported games will work. However Sony have already said UMDs aren't supported and if the only way to get the PSP games onto your Vita is through the store then I highly doubt any unofficially supported games will work.

Sorry for not providing any concrete definiative sources I just couldn't find any.

It appears you CAN install most* PSP games availible on the PSN onto your Vita if you have a PS3.

Download the PSP games onto your PS3 and then connect your Vita. Using Content Manager you should be able to use Copy from PS3 to copy over most PSP games (not Minis, not PS1 games) onto your Vita, even if they're not available for direct download.

Some PSP games are still not available however; I found some games didn't copy over via this method. The following games didn't transfer from my library (not an exhaustive list):

• Patapon 3
• Wipeout Pure
• Pixeljunk Monsters