No, you need the latest firmware (I think 6.35) to access the PSN and the games you bought from it.
There are many online vendor for psp games already available. You can just register in them for a small fee and they give you thousands of psp games to download legally. An example website is http://clocks.110mb.com/pspgames.htm
Download the latest update, and redownload the games from the PSN.
All PSP games are the same, there are no version specific games. No matter what model a PSP it is, as long as it has a UMD drive then it can play any UMD game.
You can purchase and download games from the PlayStation Network, available from the PSP's menu bar.
There are a large variety of different games which are available for the PSP 3. These games include, but are not limited to, NBA, Injustice, Beyond, and Ultimate Alliance.
the early ones and the PSP DS & PSP version games
No the PSP plays PSP games. The PS2 and PS3 games would be too complex to run even if a PSP version was made it has to be made with less capabilities so the PSP can run the program
an official release date is unknown. it's not even clear if there will be a version for the psp
Tekken 6 is available on PSP version 6.0 since November 2009.
You can not change a PS2 game into a PSP game. Games have to be developed for a Platform and each version must be developed separately
No, there are no Sly Cooper games available on PSP.
Yes, there are lots that arent on the PSP.