Thaine has you started down the right path. A couple of overall pictures would help. One photo showing the action open and another photo so that we can see the sights, if present. A photo of the upper surface of the upper tang will show us if it had a tang sight.
Looks to me to be some sort of Martini variant. It is a double set trigger action. The rear trigger "sets" the front, making the trigger pull (front) very light.
Yes, slug the bore as those dimensions vary widely. A chamber cast will tell you what has been done. Most of those rifles use some variant of a .30-30 or .32 Winchester Special case. Lead alloy bullets only.
