Well, in someone's dying moments, then I suppose it would be possible to do something unselfish. But then that brings up the question of whether or not they're doing it to help the other person, etc., or just to get into heaven.
Right, which could be considered a reward. But isn't the fact that doing something for others provides a reward shows that humans are unselfish because we're programmed - so to speak - to feel good as a result?
Could be either one. I think it's mostly relief; humans at one point probably feared that they would be punished as a result of being selfish, and now we're stuck with the instinct. *shrugs*.
I don't think someone can do something with absolutely no motive. Even churches doing charity events do it because they think they'll get into Heaven. Suicide bombers are risking their lives for their country to become heroes or whatever BS their government is spewing. Hell, the only reason I do community service is because it's required for school and looks good on a college application.