The PSP is unable to store any user data at all apart from its own firmware and any setting related to that. You must have a memory stick, before you can download games from the PSN, or even store save files.
It depends on how big the game is and how big your memory stick is. You can install a game on your memory stick just like you would on a hard drive. when you are installing the game just choose to...
No, the memory stick is the only way to store the files you want without interfering with the PSP's systems, which will definitely permanently screw up your PSP.
You don't need to download anything apart from the latest firmware updates. On the PSP's menu bar, you can access the PlayStation Network, from which you can purchase games and download them to your...
No you get PSP games on your PS3 at the PlayStation Store and then you move them to the PSP. The PSP will not play PS3 games, but the PS3 can download and store the PSP games and not play them