Hi - you're asking a lot of the right questions. I've got a desk job in DC and currently live aboard a 33' sailboat in a marina, with spouse, no pets, no kids. We moved here from Michigan and jumped at the chance to ditch the house and the stuff and move aboard - sounds like your scenario - and never, never looked back.
Others have pointed out the problems with living aboard in DC - consider Annapolis area, 5 minutes to good sailing, 45 min to DC (much more during rush hour - BUT - there's a great commuter bus to downtown) many liveaboard-friendly marinas including several DIY. You'd be surrounded by a community of other boaters you can learn from.
Others have answered a lot of your specific questions; but here are a few more thoughts.
Heat/air conditioning - there are heat pump units that are 2-in-one, heat and cool using saltwater, around $2000. When the water temp gets into the low 40s, these aren't very efficient; most of the marina liveaboards supplement with small electric space heaters.
Use a laptop; for sound, install automobile stereo and play the laptop through it.
In season, you can get your holding tank pumped out by a pumpout boat that comes to you for $5. (and/or use the marina bathroom)
Costs: well, we would have had to find a place for the boat anyway, so it doesn't really compare. A high-end slip here will cost as much as a low-end apartment, figure $5-$10K/yr depending on size of boat and marina amenities. But then again, remember that you'll be doing every day what others pay to do on vacation! PM me if you do decide to go for it, we can put you in touch with others. Liveaboards with small kids are rarer, but they're there.