That one was probably manufactured in middle to late 1901 or 1902 from the serial number. Not particularly early as far as that gun goes. VERY nice piece of family history!
These guns were shot with blackpowder ammunition with corrosive primers, so it's not uncommon to see them with pits in the barrel from corrosion.
It's as simple to determine as looking down the barrel while shining a bright light through the other end so you can look to see if there are any dark areas, if the rifling is nice and pronounced, or if there are actual pits in the bore.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.