Yes, but you will need a xbox360 live gold membership card to be able to play them online.
you download an update from xbox live but some games still might not play...
Yes.
yes it can
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.
it depends on what your into me personally i would get xbox360 live as i really enjoy that :P
Nope, Xbox360 games bought in the US will not work on an EU system.
Yes
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.
no, you only need xbox live if you want to play online
yes you can but only if you have a hard drive
personally i prefer xbox360 over ps3. xbox360 you get some games you wouldn't get like halo so that's gone. also the psp has the same thing but the games are less known. the bad part is that you have to pay for xbox live while psp doesn't have to. i can guaranteed you probably have more friends that have xbox360. Lastly i xbox360 you get "achievement's" which give you self accomplishment while psp does.
go to xbox LIVE marketplace and there is a huge list of downloads