Welcome to OCDO. Thanks for asking questions we can actually answer.
No, your friend cannot take a firearm, or even ammunition, into DC without first having a permit to posses it. DC is just barely complying with the court order to issue permits for folks to have firearms in their homes - they have no process for "allowing" folks to have a firearm outside of the home. There is a lawsuit in the courts to try to remedy that, but a decisio is still a long way off.
No, your friend cannot take a firearm or ammunition into Maryland unless both are in separate locked containers and otherwise comply with FOPA rules (which you should Google). And since he is a cabbie he does not qualify for FOPA protections so the realistic answer is stll no for firearms in Maryland.
These responses are intentionally brief and barely bother to meet the rules of citing the relevant laws involved. But I don't think you or your friend are looking for a detailed legal education, so this is what you get.
I've never bothered to look into it but there have been mentions that some of the NOVA jurisdictions have taxicab laws that are supposed to strip cabbies of the privilege of carrying concealed while on duty, and of prohibiting open carry while working. Your friend should check a site like MuniCode http://www.municode.com/resources/online%20Library.asp to see what the various jurisdictions might have done in that regard.
You are both encouraged to go look at www.vcdl.org and become members. Also, check the Virginia forum for notices of open carry get-togethers (breakfasts, lunches, dinners, trash pick-ups and the annual Lobby Day gathering at the General Assembly building in Richmond). You will get the chance to meet good folks and learn a lot.
Finally - would you consider doing a olde pharte a favor and taking a breath every once in a while? It's difficult reading one long run-on sentence.