I have a reservation for next week, and my arrival time at midway is 3:55 pm, but my reservation at Park N Fly only goes to 4:30 pm. What happens if I arrive at Park N Fly after 4:30?

No problem. There is someone there 24/7 just call them and they will adjust the time for you.

Check with them

You should be good, they don't charge until the next day if you arrive after 4 or 5. Look at your receipt.

I would check with them, but I think you're paying for the day not by the hour. I don't believe I've ever been charged for being a bit late to get the car.