I’ve never had much luck dealing with police. I’ve had mixed results dealing with neighbors. Was the guy threatening you with the gun, or did he just have it along in case there was an animal harassing his livestock?
You are certainly legal to walk your dog on a public road. Because you can doesn’t necessarily mean you should in the middle of the night, for several reasons. Pissing off your neighbors would be among these reasons.
As to the other dogs running loose and getting after your dog, a call to animal control would be in order, as dogs aren’t supposed to run loose, at least where I live anyway.
I am confused about this. You say you are in a very rural area, but your profile lists you living in Nashville. I guess both could be technically correct, but unlikely.
Good luck with t. Neighbors can be a challenge sometimes.