Will it play downloadable psp and ps1 games?
If you don't see a downloadable game you own on there, be aware that Sony is looking to get more PSP games available to play on the Vita in the coming weeks.
As for PS1 classics, I couldn't really find any official confirmation, but from what I hear: It's coming soon. There was no downloadable PS1 support from the Japanese Vita launch, and it doesn't look like there's going to be any support for it when it comes to the Vita launch everywhere else this month.
It seems obvious that the system is capable to play PS1 titles, so hopefully the ability to do so will come real soon.
Hope that helps!
Clicking the mark as good answer button helps us highlight the best answers.
Sony had a live-stream recently on the US PlayStation Blog, and they confirmed during the stream that PS1 games currently aren't supported, but they will be "soon" with no reference date at all.
Hopefully it's REAL soon!