You sure can. You have a copy on the xbox (or PS3 harddrive). You can have an additional copy if you use a removable storage device. Not many people get the removable storage device unless you like to play couch coop on different consoles.
Thats a negative. The save game is tied to my profile so it has to be logged in to play. Also other profiles or guests cant use it. The save cannot be copied only moved from hd to memory card or vice versa. The only option I truly have is to download gamesaves which microsoft considers a violation of live policy. Download somones character but live becomes dangerous to play on. It would have never been as good as mine anyway. I dont know, I think it would take the hand of god to get me to start again. Its not another character, I had a level 41 Shadow Warrior , a 141 Shadow Warrior, and a level 170 dryad. She was to be my bargaining beast, a goddes to give to my seraphim. But oh well. Games gotta go. I was surprised of the responses though, community almost made me feel good . If any 360 players would hop on and help me with some awesome hand me downs id start again. The traders were giving me all skills +24 I had rings with 2.0 sec per hit. Nevermind the 2 level 200 officer sabres. orc shocks. 3 star relics. so so much. . LAter