Nope, Xbox360 games bought in the US will not work on an EU system.
You don't need live to save games to the hard drive the game will simply ask you to create a new games save and off you go. If you have a memory card too the game will give you a choice of which device to save your game on.
Clear the cache.
No. Kohls does not sell any gaming system console. However, they do sell the games.
yes it can
Yes.
yes you can if you sign into the playstation network and download a game
No.
Yes
yes it will just be hard to navigate through the dashboard.
A Xbox360 is a console, the second after the first Xbox. You play Xbox360 games on it and I think you can download or buy a thing so you can play your Xbox games on it to.
yes you can but only if you have a hard drive