Look at the rifling in a good light. If it seems washed out or severely pitted, it may be "shot out". If the grooves have buildup that won't clean out easily, it may require that lead be removed. This should only be a problem if you have been shooting cast bullets (not jacketed).
Sights, barrel and bedding.
Unlikely that it is shot out. Have it examined by a competent gunsmith
Unknown.
All guns should have the information stamped onto the barrel. Most of the time it is near the action. Look on the barrel of your shot gun and it should tell you the make, model, caliber (or in your case with a shot gun) the gauge, for shot guns the size of shell the gun takes, and finally the choke the shot gun has. If it is a screw on choke it should saw on it.
I don't think there is a way to visually tell the difference between leaded and unleaded fuel. However, leaded gasoline has become "extinct" and it is more likely that you have unleaded gasoline in the can.
So do I!
Most likely a "store brand" shotgun made at the turn of the century.
how to tell the age of a 12 gauge single barrel shot gun made by American Gun Company?
70-100 yrs
You inspect the parts to see if they look worn. If a gun has been shot once or twice, or a very few times and then cleaned, it may be hard to tell if it's been shot, but if it hasn't been cleaned, there will probably be fouling inside the barrel.
It says it on the barrel, otherwise if there's no riffling it's been modified or shot out, but quite unlikely.
As long as the barrel was made after 1950 and does NOT have a full choke, you will be able to shoot steel #2 or smaller.