Nice report - good mix of photos and text and a nice read.
Can you tap your card to pay in Washington? Hell no, you've gotta buy a Metro card and then load credit on it. It was very antiquated and it took us a few minutes to work out what we were supposed to do. But eventually we were on the Metro and headed towards Smithsonian where we were going to get off and see a couple of the sights.
Perhaps not obvious but you can add a transit pass for the Metro from within the Apple wallet app on iPhone (and I believe via Google Wallet on Android). Works great and non rush hour fares are a flat $2 each way so it’s easy to figure out how much valid to add to the pass.