American rules on gun ownership?

It is often a state and local issue and not an "American" one.

Some counties, even in a gun hostile state like California, make gun licensing and carry permits easy. While in the county right next door you can only get a carry permit if you make rather large contributions to the right political races.

So for your story you can make the rules just about as lax or as strict as you would like.

As far as the USA as a whole the only guns that require a permit to own are short barrelled rifles & shotguns (under 18"), full-auto or selective fire weapons and silencers.

The various states have more restrictive gun laws but most if you have a clean record you can walk into any gun shop and buy any long gun or handgun you want.

Here's a good overview of the state's gun laws. https://www.nraila.org/gun-laws/

For most of the USA you do not need to get a license to buy and own a gun. You will need to pass a background check. There are a few states and locales where you would need a gun license to buy or own a gun.

For most of the USA, you would need a permit to carry a handgun, though there are states where no permit is required. And most states that require a permit will issue them if you pass a background check and get a few hours of training.

If you live in a rural area and have lots of property, like a farm maybe, you can shoot on your property. Otherwise most of us either go to a shooting range or some deserted area of public lands to shoot.

There are generally no restrictions on size or weight, but full auto weapons while technically legal to own, are basically banned because of restrictions and cost.

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