well, i work there, as you may know
1) weekend shows can vary greatly. i wouldnt say they usually end by midnight. midnight would be the earliest (i wish they ended earlier!) they are usually done by 1am though.
2) its a perfectly fine area. its a bunch of drunk college kids (and therefore tons of cops everywhere).
3.) no. not near any public transit. well, its close to metro (about 3 blocks to Shot Tower) but if you're coming from DC thats not going to help.
other than that, Judge Alito is right, train from Penn Station. but theres many parking garages nearby if you have a car.