No they can't.
You can see a list of compatible games by following the link in the Related Links.
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Yes, it will work. I have an xbox 360 and ! always play normal xbox games on it.
Yes the Xbox version of the game works on 360 but it must be the original copy. Just know that any mods you can add for the game on Xbox dont work on 360.
No, original XBOX controllers do not work for the XBOX 360.
No they do not, but you can play certain Xbox original games on Xbox 360
No, but some original Xbox games work for Xbox 360.