You can't delete your own node (you could delete the contents, but this is generally considered an abuse in itself). It is possible for the node to be considered for deletion, though.

I've had my own nodes downvoted for no reason I could figure out (perhaps somebody wanted to use up their votes and decided the -- button was slightly closer to their mouse pointer's position), but its usually only one or two points. -5 to -10 indicates a serious problem. I would like it, though, if people would at least message me or reply when they downvote me.