Is that what these tiny holes are extreme right and extreme left in the pic, for pins? They're so small, what do you use to punch them out, and does direction matter or are pins typically symmetrical.
A 1/16” pin punch should be about right. Lowe’s, Home Depot or other hardware store should have them.
The pins are normally symmetrical, but I have seen one old gun made in Eastern Ky, that had tapered pins, but it was obvious because the holes were bigger on one side of the gun.
but why would I want to take the barrel off?
Curiosity? If the barrel maker marked the barrel, the markings will likely be on the bottom of the barrel. And given the crud build up on the rest of the gun, it’s likely crudded up in the barrel channel, which can be a good environment for rust. Remove the screw from the barrel tang, then remove all the barrel pins. I'm guessing there will be at least 3. Spread a towel on a level surface and place the gun, barrel down, on the towel. Now raise the butt just an inch or so with one hand, and tap your other hand against the comb of the stock. The barrel should begin to drop out. Be careful with the fore-end of the stock, it's fragile and the barrel may be stuck to the wood with crud.
Besides, you should learn all about your gun. It’s the journey. Have fun.
-Ron