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
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Your thinking about the PS3 not the PS2. The PS2 can not connect with the PSP as they don't work together
You do not convert a PS2 into a PSP. I don't even understand the question. Do you mean the PS2 games they are PS2 games and will not play on a PSP. A PSP is a Portable Playstation and if could use take a console like the PS2 and turn it into a Portable it still would not be a PSP. Back to the games a PSP is not able to play PS2 or PS3 games because all the hardware needed is not included in a PSP. Even the new PS Vita will only play newly designed more complex games that are still not up to the level of PS2 and PS3 game.
No you can not make a PSP play a PS2 game. You can't even make a PS3 slim play a PS2 game or the Fat PS3 models made after August 2008 with 2 USB Ports.
No the PSP can not play PS2 games
It is a PS2 portable which means good graphics, it is portable(obvious), It has internet on it, and you can plug it into a PS3 and play PSP games.