Yes, you need XBOX Live in order to do so.
No
U do not need xbox live I'm sure I'm just 9
yes, you need to pay to do anything on live
Yes for the Xbox 360 game you do
No you do need to be connected to the internet and have live silver
You need Xbox live to use any sort of DLC.
You can play single player zombies without Xbox Live, but you can't play online with other players unless you have Xbox Live.
the RC-XD is usable in Local mode without Xbox Live you just need to get 3 killstreaks but if you want to play online you need Xbox Live and you need to buy the killstreak
yes unless you have the newest xbox 360 (black slimline), If not you have to use either an adapter or a ethernet cable
yes
you need to have xbox live