Can you play Xbox games on the Xbox 360?

Answer 1

Yes,

Assuming that you have a hard drive accessory, any Xbox360 will play certain original Xbox games. You can check the list for a specific game by visiting the following link:

http://www.xbox.com/en-US/games/backwardcompatibilitygameslist.htm

If you try to play games that are on the list, provided by the above link, please make sure you have access to the internet on your Xbox 360. This will update your 360's list of compatible original Xbox games. If this does not work, please click here

http://www.xbox.com/en-US/games/backwardscompatibility.htm#disc

Then click "Burn a DVD or CD." and then follow those instuctions. In a nutshell those instructions show you where to download that update, and how to burn it to a DVD, or CD that will work on your 360.
Yes! Of Coarse!