Sure can.
Yes. It is an Xbox 360 game.
Yes and Portal 2.
Yes, you can play online coop with up to four players.
No. It doesn't has coop support today and most likely will not have in the future either. Good database of coop games can be found here: http://www.xboxmp.com/
I have not played Dead Island but My answer is no you cant play coop without Xbox live and maybe you can if u have spare controllers those are my best suggestions but it is stupid that u need this Xbox Live on these things
No
Yes. Add KSHARP142
Yes. Portal 2 is on Xbox 360, PS3 and PC.
No, Portal 2 is also out for PS3 and PC.
No Portal 2 is for PC, Xbox 360 and PS3.
Yes.
You can't.