It's hard to say for sore that it's not a ball type fishing weight, but I can see it being a musket ball puller as well. I'd think a ball worm would have done more damage.
Huh, hard telling.
Puller can not be seen . It would resemble a screw and be imbedded in the ball ( out of sight) in your picture.
Could be that someone pulled the tip off their ramrod trying to pull a ball. In which case a cross pin ,or a hole for one on both sides of the ferrule should be evident and loading rod of wood pulled off pin. A metal rod could have failed from corrosion but wood is more suspect.
Measuring/guaging ball could bring guess closer if a common previous dimension. Example ,today's .50 cal. roundball can be .490-.495.
Early nonswaged roundballs often show a sprue and mold line around their equator. While they could be rolled between plates to smooth seams and sprue after trimming short ,that would be labor and equipment costly while not really needed for common use.