No there is not. Try Panda Parking for discounts on parking and availibity.
Nope, I personally would seek out a parking lot nearby before you travel.
Reagan building also has flat rate ample parking
Use the Metro. Closest stop is Smithsonian, which has Blue, Orange and Silver lines. The Metro is fast, clean, cheap, easy and safe. I can't imagine trying to park near the Mall.
There is not parking onsite. Because it sits on the national Mall, however, it is not terribly far from a metro (subway) stop. If you are bringing a large van or bus be sure to do your research before you come. Our driver planned to park in a garage, but it turned out the van was too tall. A lot of the street parking near there has a 2 hour limit. 2 hours is not nearly enough time to see the museum.
Nope
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