Hi CA2DC, welcome to the forum and welcome in advance to DC. Im not an expert DC commuter, but I think I can get you going in the right direction. There should be plenty of others here to help you. Until then Ill do my best.
I think the first answer to your question could help with your other answers. http://www.capitalbikeshare.com/ I dont personally use this but there is plenty of info on their site. Its set up so you can grab a bike, ride it to wherever, and drop it off (providing there is a station around). You can sign up for a few days, weeks or a year.
You can take a bike on the metro, BUT only during NON-rush hour times (7-9) and (4-6).
DC is pretty flat. Nothing like CA.
You can google bike routes for the area, others may have specific streets for you. I would say DC is very bike friendly compared to other large cities. It just depends where you are in the city. WABA has a route planner http://www.waba.org/resources/maps.php.
I hope this helps you out. Enjoy DC while your here.
-Jon