A new day has dawned, which means: 10 more turns! w00t!

Turn 1-8: battle in Sector 1 Reactor
Turn 9 and 10: Move on to battle at Sector 5 Reactor

I have a couple questions as well, can u post all the possible random encounters and then if we see a battle we would not like to use our offensive materia in, we can tell you so we don't waste MP? And also, after you level are you healed to full?