Yes
I am not sure. I know they have a van that takes people to & picks them up from a nearby Metro statio, but I don't know if it takes people to either Dulles or National Airport. If you call then hotel directly I am sure they will give you a definitive answer. FYI if they don't try State Shuttle. I've had great experiences with them in several states. They are reasonably priced , esp for longer rides.
Thanks! Your answer is awaiting moderation.