All the xbox back catalogue should play on the 360, however you may need an update over xbox live to get some to work.
No that is why it is called a PSP game and not a Xbox 360 game
I don't think that you can play an original Xbox game on an Xbox 360 live. But some games from the old xbox you can play on Xbox 360.
Yes
For you to be able to play the game itself - no.
if you have a x box 1 no only works on 360 version
Dawn of War II cannot be played on the Xbox 360; it is a PC game only.
Yes. you can play ANY xbox 360 game on ANY type of xbox 360. you can also play original xbox games on the xbox 360. (but you have to have a hard-drive to play original xbox games on the 360)
Yes, but not all of the original XBOX games. You can either download the ones that are able to be played on the XBOX 360, or put in the disk to the games that are allowed to be played.
No, an Xbox 360 game will not run on an original Xbox.
Yes Im almost 100% sure you can.
An individual with an Xbox 360 is not able to "talk" to a game mod. An Xbox 360 game mod (also known as modding) is a type of chip or modification that allows a user to play "burned games". This means a person copied the game to a device. These types of games cannot be played on the standard Xbox 360. With a mod (or modification) the Xbox will accept these game formats. Therefore, a person cannot talk to a mod. A person can install or perform a mod, but they cannot talk to one.
Nope, the 360 wont be able to read the game.