no
You cannot, you must have a separate disc for the different console.
No. All games are marked because they fit for the specific game console. The product is made especially for the Xbox, but if you want to play it on a PS2, you could try finding the same game for the right console.
You can not play PS3 games on a PS2 console
No PS2 games do not play on the Xbox or Xbox 360
Xbox 360 games do not play on the PS2 or they would be called Xbox 360/PS2 games
No the PS2 does not play Xbox 360 games only the Xbox 360 plays the games for it.
You can play original Xbox games on the 360 because it is backwards compatible but you cannot play any other console games on the Xbox 360 because it does not support other discs. There would be no point in other discs if you could play one disc on any console.
No it can not play PS2 games
No the PS2 does not play burned games
No the Xbox 360 can not play a PS2 game
No you can not play PS2 Games on the Xbox 360
If there PS2 educational games. The PS2 will not play games not designed specifically for the PS2 console