If I feel someone MAY be a threat to me, can I show them that I have a gun to scare them off?

Any action you take with a gun must be in direct self-defense; otherwise, it may be considered threatening with a dangerous weapon and you could be labeled as the aggressor. You may be criminally charged and you will possibly have your permit revoked. Carrying a firearm is very serious business. There is no room for mistakes. If you pull a firearm on someone or even display the weapon, then it must be in self defense or it is not justified.