I did not see any no fee parking. Ask park officials if they will allow a photo shoot. I am sure as long as you are out of the way it is okay.
Parking is limited around the Navy Yard area. Ask a park ranger and a Navy sailor where pictures can or cannot be taken.
No fee for parking, and admission to the USS Constitution is also free. Would not need permit around the waterfront to take photos; not sure about on the ship, but there are security measures in place - x-ray machine, metal detectors, etc. - so you'd likely need some clearance from the National Park Service and/or federal govt in order to bring in equipment and shoot.
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