Appeals are easy in high school rules because they can be made while the ball is live or when it is dead. Other rule sets require the ball to be live but NFHS does not. And the appeal doesn't have to originate on the mound. Just tag the base or the runner and state what you are appealing.
There is no penalty for an unsuccessful appeal or even multiple unsuccessful appeals on the same play.
Umpires should never say or do anything to alert a team to the potential for a successful appeal.
On rare occasions, players or coaches ask if they should appeal something. It's rare because it's just as easy to make the appeal as it is to ask about it.
Recently, I granted time after the batter-runner fell down while rounding first base and limped into second base in obvious pain. While he was being tended by the trainer, the defensive coach ambled over to me and asked if there was any point in appealing the touch at first. Since I had seen the player trip over the base, I advised the coach to save himself the trouble.
Another time, a runner left third early on a fly ball to left. After the runner scored and headed to the dugout, the catcher asked me if he had left early. I told him there was a procedure in place to get my opinion on that question. He figured it out, made the appeal, and got the out.