Yes, you can definitely sleep in the airport and wait for your flight. The last flight arrives at about midnight and the first flight out is at 5:00 AM.
You can if necessary. The only facilities are bathrooms and vending machines. However College Cabs does have cabs available 24 hours so you can get a ride into or back from town if you needed. They also deliver food if you need it for a fee if that's all you needed.
You can sleep in the airport, though I wouldn't recommend it. It's still an airport so if someone decides your bags are theirs while you're asleep then they're gone.
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