If your gun has no engraving, it very likely doesn't have Damascus barrels. In the Model 1889, only the higher grades (engraved) had Damascus, which was considered a classy and valuable feature. Yours probably has their "Compressed Fluid Steel" barrels, which are forged solid steel. Remington nuts argue about whether these are stronger than their excellent Belgian Damascus, but the argument is unresolved as far as I'm concerned.
One thing you CAN be sure of is that this gun wasn't made for steel shot. Another is that it is most likely chambered for 2 5/8" shells, unless it is stamped "for 2 3/4" ctg." somewhere or has been rechambered. If it is a 10 guage and has "Magnum" stamped on the barrel flats, it has been rechambered either by a gunsmith or at the factory to the "old magnum" 2 7/8" 10 guage shells. This was a fairly common conversion back in the day. DON'T EVEN THINK of firing a modern 3 1/2" 10 Magnum in it!!!!!
If it is a 16 guage, you have a very rare bird(gun)!
With a serial number like that, I'd say the gun was made about 1902-3 (a guess), but in any case, it is fairly late for an '89, and in the period of transition to smokeless powder. If it were mine, I'd shoot only low pressure 2 1/2" shells like PolyWad or RSI "Vintagers" or black powder in it.
Sorry I can't provide more detailed answers to your marking questions. But if you don't get detailed answers here and haven't yet posed your questions to
www.doublegunshop.com/BBS on their "Double Barrel Shotgun" forum (the first one), you will get answers there.
There is also a book on Remington SxS doubles; I don't have it but I believe the author's name is Semmer.
Good luck, neat gun!
Mike Armstrong aka Mesa