The closest it over 1/4 mile away.
My neighbors are so used to gunshots at all hours that it would be nothing unusual. Besides, they are a half mile away.
Depends on the rural area.
I have a relative who lives on a small farm. The fields are behind the house, neighbor is just across the road, with more neighbors and non-farming homes along the road. About a dozen households within 100 yards.
Distance nothwithstanding, you should try to cultivate friendly relationships with your like-minded neighbors. There is strength in numbers, which is why humans have tended to gather in communities since the dawn of time.
The work can be shared, ideas and skills can be shared, and people can work in shifts if necessary (such as the neighborhood watch).
Twenty, fifty, a hundred people working together with good leadership can do a lot more toward survival, comfort, and safety than a bunch of individual people, couples, and families on their own.