Skeeterbd, welcome to a great site where there is a vast amount of knowledge.
From the markings on your barrels water table of "13" that would be bore. It could be from .710 to .719, I believe. Anything over that and it would be out of proof (from honing). I can't quite make out what the choke markings are.
Sir Joseph Whitworth steel was the best you could get.
An F4 was a medium priced gun at 35/40 gns., and is the Third System of Grading from 1893-1903.
Your serial number dates it to 1900, and there were a total of 919 guns made that year.
The dent should be easy enough to fix and I'm sure it will not hurt anything, but the barrels wall thickness should be checked even if it didn't have the dent.
Good luck with it and thanks for sharing, and I'm sure there will be other more knowledgeable people helping you out.
