#1 - To refresh the new day's appointments, tasks, etc. I don't think you can stop the iPAQ from waking up at midnight. Change the clock
#2 - I don't think there's anything wrong. My iPAQs all do that and so do my friends'. I'm not sure if there's a way to just flash the LED and not switch on the PPC.
#3 - I believe that the CF Expansion Pack Plus's battery actually powers the iPAQ but the PC Card one's battery powers the PC card only. Thought I'm not 100% sure on that.