Maryland is a compact state, but DC is not, so you will need a DC license in order to work in DC (however, if you don't want to work in MD, you don't have to get a MD license!
) You can apply for DC licensure by endorsement whenever you choose, once you've passed NCLEX, or you can skip MD entirely, apply initially in DC, and take the NCLEX through them.
You can hold as many different licenses as you care to pay for (and meet the other requirements) -- the only exception to that is the compact states; you can't hold more than one compact license at a time. Maryland will have no interest in you applying for DC licensure.
With a Maryland license, since it is a compact state, you can work in other compact states with your MD license as long as you maintain your permanent residence in Maryland. If you move from Maryland, you'll need to apply for a new license in your new home state, even if it's another compact state. People get v. confused about this, but it works exactly the same as your driver's license -- you can drive through, or around, any state in the US with your home state driver's license, but if you move
to a new state, you have 30 days (or whatever the state law says) to apply for a new license. You can't just keep driving indefinitely on your old license. The only reason that is possible, and we don't have to stop and apply for a new license at each state line when we're on vacation, is because all the states got together a long time ago and all signed a compact
agreeing to recognize each other's driver's licenses. The Nursing Licensure Compact (NLC) is exactly the same thing, except only a limited number of states have chosen to join so far.