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If I start a game with 11 batters, can I add Johnny to the bottom of the order when he finally shows up? (Now 12 batters). Or do I need to start with 12 and skip him until he shows up?

You can add players only until you have made it through the lineup. Once you get to the top of the lineup you cannot add an additional batter. So your best solution if you know the player will be late is to include him in the lineup and skip his turn as you suggested.