First you have to have Xbox Live and then go to "game marketplace" and look up the game you want. Get Microsoft points if you don't already have some then wait for it to say it has downloaded. Go to game library and it should be there.
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In order to play games for the original Xbox on the Xbox 360 you will need to have the hard drive. This is because the update is downloaded onto it.
You can't.
If you want to get banned then yes.
The Xbox 360 can play original Xbox games but the Xbox doesnt play Xbox 360 games.
No the PS2 does not play Xbox 360 games only the Xbox 360 plays the games for it.