When it asks you if you want to heal after battle it uses up all the points you have left over. Seeing as they get discarded after the battle there is absolutely no downside to it. The main thing is making sure you finish the battle with extra magic so that you can take advantage of this. If you finish with no magic then you don't get any free healing after battle.

Enemies don't counter attack, but IIRC they can occasionally slip their turns in the middle of your chain if you don't have all the commands input quickly. But not very often.