There's no way to diagnose the coolant leak over a computer without seeing it, but the battery light is on because the generator has stopped recharging the battery. It is run by that belt, so yes, you do not have a charging system problem. The belt is the cause of the battery light. The power steering pump is also driven by that belt so all that's needed is to get the belt back on.
You didn't say which engine you have. If the water pump is driven by that same belt, the engine will overheat within a few minutes and the coolant will expand and / or boil out of the reservoir. That will also be solved when the belt is reinstalled. On some engines the water pump is run by the timing belt so the engine would not overheat if the serpentine belt that you mentioned fails. In that case the coolant is a different issue and would likely be the cause of the serpentine belt slipping off. Reinstalling the belt in that case would not solve the coolant problem.
It's doubtful the belt problem was caused by a missing shield. Those are to keep fingers out of dangerous areas and to keep snow from getting impacted around the belt. The belt is going to get wet in rainy weather regardless if that shield is in place or not. There's a good chance a pulley is out of alignment or a spring-loaded tensioner pulley is loose or weak. The additional clues are a squeal from the belt when the engine is running. Or there's signs of fraying on one side of the belt.
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Saturday, November 2nd, 2013 AT 2:07 PM