Remington is not too forthcoming with serial number data. The date codes on the side of the barrel would have to be PN or RN there is no FN code. The first letter denotes the month of manufacture. The second denotes the year. PN would be June/1922 and RN would be Nov/1922. I have no idea what the etched R indicates since it isn't factory applied. Perhaps you could post a picture? You should have the version with the safety in front of the trigger. Later models had the safety moved behind the trigger in the trigger guard.
The Remington Model 11 was a J. Browning design that was manufactured by Remington in the US while FN Belgium was manufacturing the A5 for sale in the rest of the world. There were a few minor differences between the Remington & FN offerings. Screws are not interchangeable for instance since all Remingtons had SAE screw pitches and Belgium Brownings had metric screw pitches. Interestingly, during WWII when Germany had appropriated the FN plant for their own purposes, Remington manufactured the A5 at it's Ilion, NY plant right alongside the Model 11 until after the war. Additionally, FN made some barrels for Remington as I have seen a number of Model 11 barrels stamped FN, Made in Belgium, but with the Remington Model 11 designation. At one point, Browning also licensed Savage to make this same firearm as you will see Savage model 720 shotguns occasionally and they are the same clone with only very minor changes. Remington originally produced the Model 11 in 12 and 20 gauge with 16 gauge being added in 1931. Remington ceased production of this model in 1948 when they introduced the Model 11-48. The Model 11 has the distinction of being the first U.S. produced autoloading shotgun. It was in production from about 1905 through 1948.
By all means download the operating manual. There are two friction washers that travel on the magazine tube that have to be correctly installed depending on whether you are shooting field or target loads. If installed incorrectly, it can lead to a cracked stock or cracked forend or both.
It is not the easiest shotgun to completely tear down and clean, but there are a number of references available to assist you. Once you've done it, it ceases to be intimidating.
Outside of cracked stocks and forearms, the only parts that ever seem to wear on these fine old shotguns are the action spring and the recoil spring. Thankfully, these parts will fit from an A5. Enjoy the old girl and shoot her regularly. They are wonderful examples of gunmaking at it's best.
Don
