I'm not sure how Maryland does it but it is unlikely that they will demand that you pay DC tickets to renew Maryland plates. I know that Virginia doesn't require out-of-state tickets to be paid (unless you have a warrant or something
).
As for transferring tags between vehicles, I don't think Maryland does this, the tags belong with the vehicle (unlike Virginia, where they are transferable). The Maryland tags (and tag numbers) are issued based on the type of vehicle, so you can't transfer tags from one vehicle to another as far as I know. Perhaps this is different with custom plates though.