Well, dealing with the light issue, it seems obvious enough to me that if the staff fell. He could easily have grabbed it and relit it. Here's the scene in my mind. Glamdring is on his side. Since in theory he'd use both hands when breaking the bridge with the staff. He drops the staff and grabs the bridge and fell. The Balrog probably pulled Gandalf closer to him when they fell, since he was tied to the whip. And when they hit the water, Gandalf easily could have looked up and seen the staff or the sword falling ( I assume the combined weight of the two was enough to beat out the sword and staff). Depending on which one he sees he could have grabbed one of them. And the Staff would in theory still be giving off light. So that would be easy enough to see .

