You could dry camp below the dam in the BLM area. Call the COE visitor center (505-685-4371) and ask the rangers about the road below the dam-- it's often pretty rough and at its best it is not suitable for a large motorhome.
I don't believe so. The entry gates will be locked I think. The best way (or a way) to find out is go to recreation.gov and see if it will let you reserve the day(s) you want.