If you have accidently deleted a game you have purchased from PLAYSTATION online you can simply go back to store and check out your recent purchases/downloads and you can redownload it as long as its been purchased
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If you buy a game on the PSN, you can delete it whenever you want - all you need to do to regain it is go back on the PSN and redownload it for free.
If you have downloaded games for the PSP Go into your PS3 they will work with the PS Vita also
yes
No, all you need is a wireless internet connection. The PSP can connect to the PlayStation Network from its menu bar, the games are purchased and downloaded from there.
The PSP Go does not have a UMD reader, you cannot play a UMD game on it.