There’s a metro station at DCA, on the blue and yellow lines. Just checked and it seems to be running as normal. It depends where near the Mall you’re staying but yellow line might be a bit faster.

For Udvar-Hazy, I don’t know that there is a good way to get there via public transport (edit: I see someone else posted the link, yes needs a connection) so might need an Uber/taxi. I prefer Udvar-Hazy to the Mall portion of the Air & Space museum.

Be warned there may be no food/drink at Udvar-Hazy at the moment. I was there a couple months ago, they had closed the old McDonalds that was there and refurbishing and getting a new food place in timing was TBD.