I began the quest "Some Light Left" and stole the Arcane staff for Malur Seloth, but I want to keep the staff now that I have it, it is a lot better than one more level in Speech. Should I leave the quest as unfinished and try to find and complete another quest in Winterhold to become Thane, or is it possible to give him the staff and then quietly assassinate him (maybe an arrow from afar? and I never liked him anyways)? Stealth archer class btw

Save before giving the staff and kill him to see if you can get it back. If you can't, reload and let the quest unfinished. You can help members of the college in order to become thane. When I became thane I did Brelyna's, J'zargo's and Sergius' quests.