If you're talking about achievements... You can only delete those if you've earned 0 achievement points for the game... Any higher and you cannot...
If you're talking about games you installed on the hard drive, you have to go to system settings -> memory -> choose which one you installed the game on -> games -> click the game name -> should be 2GB or higher and should say Xbox 360 game or something similar below that... delete that one because that's the installed game...
You can do the same with games you've installed from XBOX Live, as well...
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The Xbox 360 can play original Xbox games but the Xbox doesnt play Xbox 360 games.
No, only Xbox 360 games work on Xbox 360.
You can not play xbox 360 games on an original xbox, however you can play some original xbox games on an xbox 360 console.
Your Xbox should ask you to delete an avatar when you run out of space for one
No the PS2 does not play Xbox 360 games only the Xbox 360 plays the games for it.