a lot is possible, if you stay away from the mainquest.
Yep. You just need to pick and choose your quests, and it helps to have already played a character that knows which quests are combat-centric.

For example, radiant quests from Inns are all kill-based, as are some of the Guild quest lines. However, Bard's College, and follow-up quests, are all doable without killing/aggroing anything. I wish there were more radiant quests that involved bringing an item back to someone, as those can usually be done without aggroing/killing.