You have a muzzleloading English "4 bore rifle". Now it may be closer to a 5 bore, but they were often called "4 bores" in the such sizes as you have.
A "true 4 bore ball" is 1.052. Some guns were measured at the grooves and some at the lands.
So in the terminology of the time, a "4 bore' just means it's not supposed to be a 5 bore or a 3 bore.
A 3 bore ball is 1.157"
A 4 is 1.052
A 5 is .995

As you can see, there's a lot of leeway here.

How deep are the grooves?
I would love to see pictures.

As far as it being for balls or bullets, I would have to know about the twist and the geometry of the rifling.
As a rule, very wide grooves and narrow lands were best for balls and wider lands were best for bullets. The twist is also a factor. In the days when your rifle was made, there were any number of makers experimenting with twist and rifling forms.

I would have to guess the intended market was India, but 4s were used in Africa too. As light as you rifle is, I would have to guess India, but it's just a guess. I believe more 4s went to Africa than India, but as I said, it's just a guess.
Most 4s I have seen were much heavier than 11.5 pounds. in fact, close to double that would be "average. I have seen several that were about 17 pounds and some were 20-22 pounds.
I have made some myself, and I think a 15 pound 4 bore is TOO LIGHT. However, the ones I made were rifles for balls and used charges of 350-400 grains. If your gun is rifles to use a 200 grain charge (or less) it might not bee too bad to fire.

Contact me directly if you want to chat about it.
I have a little bit of knowledge of these things. More than I really want.

(Of course, 1 shot from one of these guns is more than I really wanted.)