I disagree with the suggestion of a gun. The legal instances in which you can actually use it are minimal, the chances it will be used to hurt you or will hurt the wrong person are huge. But when I hear your story, I picture those movies where everyone in town is feeling threatened yet the girl goes off by herself in remote places, or changes in front of windows with blinds open and everyone says, "oh, come on...she'd never take that kind of risk!". Why the heck would you hang out alone in woods and at resevoirs when someone's stalking you? Be with other people. If you like to run, get a treadmill, go to a club or join a running club so you have other people to run with.
There's nothing safe about what you've described at all, and no, having a dog does not make people normal. Weird people do some normal things - it doesn't make them mentally healthy!