No, you don’t have to pay for tickets to see the National Air and Space Museum in downtown DC.
https://airandspace.si.edu/visit/mus...sked-questions
Parking nearby is problematic, but it is within walking distance of the Metro, which isn’t free either.
However, you do have to pay to park at Udvar-Hazy, although the museum itself is free. I’m told this arose because people realized that if they could park there for free, they could then take a taxi to the nearby Dulles Airport, go on vacation, and not have to pay for airport parking. The airport did not appreciate this trick.