Yes there is a lot to do with personal guns in all of the above wars.
For one, perhaps on the side of the British regulars it is only about soldiers carrying guns. But from the perspective of the colonists, it was the regular citizens having guns that stood up to the British regulars (although not very well in every instance).
For two, many of the young lads that went over to Europe were carrying Government Issue weapons. But they weren’t a whole lot different than the weapons the young men grew up with. They still had sights, fired bullets, recoiled, and were deadly.
It takes time to train a soldier. And it takes money. In order to defend itself a country must either maintain a standing army, or have a way of quickly calling up an army. Maintaining a standing army is a horribly expensive burden on a nation (might have something to do with the economic decay in American cities and the consequential gun violence). And having an army on reserve is cheaper, but getting the men trained quickly is a challenge.
That challenge of training men is all the more simplified when the drill sargeant doesn’t have to explain to the young boys which end of the gun is the dangerous end.
Yes I honestly think the Catholic Church could be in favor of people other than police and military having firearms. There are a number of teachings she has in the catechism that support it. For one, those who have the grave duty to defend others have the right to use arms. As long as I’m responsible for the safety of my family, I have a right to use arms. Just because there is a police force out there to help me with my duty doesn’t mean I’m relieved of my duty.