How do run rules, tie games and protests work?

These are largely state association decisions under NFHS rules:

• Run rule and shortened games (4-2-3): a state association may adopt game-ending procedures, including run-ahead rules and suspended games. If your state has none, the opposing coaches and the plate umpire may agree to shorten or end the game at any time.
• Tie games (4-2-5, 4-2-6): a regulation game that's called with the score tied is a tie game, unless the state association has a tie-breaker or other game-ending procedure.
• Protests (4-4): whether protests are allowed at all is the state association's option. A game started on a non-regulation field can't be protested for that reason.