Nicholas, National Parks are treated like any other public place, not like national forests or blm land. Pretty much, the rules on carrying a firearm in a national park are going to be pretty much the same as carrying on main street (unless the state has instituted national park specific rules).
If you are in a state where open carry of a loaded pistol is legal, you shouldn't have an issue.
But if the state doesn't allow open carry, you might have to conceal, which might mean a permit, and if you can get a concealed carry permit in your state it might not be honored in other states.
Discharging is definitley not legal.
You used to be able to open carry an unloaded firearm in California, that is no longer legal. So you can't open carry in Yosemite. You can conceal carry IF you have a concealed carry permit but good lucky getting that in California unless you live in some rural, semi conservative county.
Not trying to start a big discussion here, just trying to clarify! Hopefully I didn't say anything that was false.