I have a military tenant who will be moving out early due to orders. His 30 days goes into mid August, so he will be paying rent for the month of August. He is actually moving out on the 3rd, so my question is if we are able to rent the home out before Sept 1st, and get an early move in applicant would we pro-rate and give the past renter a portion of his money back? This is just a what if scenario, but I presume this is the correct tactic?

You can't double-dip rent, so yes. Check your own state's laws, but this is what we would do.

Yes you are correct, you can't collect rent from 2 different people for the same time period. That is the law in most states and I would pressume Florida as well.

Yes, of course.  Not to mention, if he's military, and moving for military reasons, there are probably all sorts of protections he has.  Why not just give him a break, accept his notice, and just advertise it for rent now?  He's serving our country, and their pay is low.