Games can not start without all players agreeing and press READY or START. This is hard-coded into the game and the game will kick you if you don't press either READY or START within a set period of time.
It is very rare but it is possible for an enemy to have three turns in a row depending on what skills they used. For example if you used only a basic, then they used a basic but they had higher agility, they could go again. Then if they had a repeat pearl, they could get another turn thanks to their Pearl for a total of three in a row. You may want to consider increasing your agility to prevent enemies from getting an extra turn when you both use the same attack.
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