Is the "No. 2811" the serial number or is there is somewhere else I should look for it
It should be the serial number, but of course, I can't see it, and don't know if it is just another military marking.
As for the barrel, I don't see any markings that jump out, maybe a real M1911 collector will jump in and give an opinion.
There may be machining marks or contours that are unique to the older pistols, rifling characteristics, I don't have one that early to examine, someone who has will have to give an opinion.
If the finish is original bluing, don't ever have the pistol reblued. The collector value of a reblued pistol is about the value of a pistol with no finish remaining.