1. If there is no hatch or door covering the entrance of the shaft, then players will not see it as someones, and they will go down and explore. There's nothing we can do about ores being mined, as they are the servers, and can't be claimed by anyone, unless you place protection stones around the area. Just place a door blocking the entrance to the shaft, so no one can get in.
2. If someone is building right outside your town, it's best to ask them to move and build somewhere else if you need the space, because it could be seen as griefing. If you ask them nicely and they don't move, just ask a Moderator or Operator to handle it.
Hope this helped