It is impossible to evaluate that pistol without good pictures of each side and of the markings, but this might help.
Lugers were shipped from the factory with two magazines numbered to the gun (including the letter suffix if any). Over time, most of those magazines were swapped or lost and replaced, so a Luger with one matching magazine is uncommon today and one with both magazines is quite rare. Most collectors want matched magazines (and will pay more for them), but will overlook the mismatch if the gun is in nice condition.
The double date stamping came about when the post-WWI German government tried to round up all the military weapons in the hands of veterans and civilians. They first paid a bounty and many weapons were turned in; when the bounty was cut off, the turn-ins dwindled (duh!). The law mandated that all guns in military and police inventory as well as those turned in be marked with "1920", the date of the law. It really was not a date, but more like a government property mark. Judging by the number of WWI Lugers captured in WWII that do not have the "1920", it is obvious that the requirement to mark all the pistols in inventory was not widely followed.
I am not expert enough in military markings to dispute your reading, but FWIW I think the first number is always the regiment number, then the regiment type, then the squadron or company, then the gun number. So I would read 4./R.R.11.16. as Fourth Reiter-Regiment, Squadron 11, weapon 16.
Jim
