Hi! I keep starting this answer, but it never turns out right. Third try!
I worked the midnight shift for most of my career as an airport police officer. Most of the time it was boring., esp. between 1 and 4 a.m. We could find someone to talk to or something to do if we really wanted to. There was some frustration, because the airport wanted us there just in case something happened, and didn't want us looking for something to get into, whereas we wanted to keep our skills up by "practicing" on traffic stops. It's not easy to fall back on academy training if something bad happens, esp. if you have been out of the academy for five years and never handled anything major. Staying sharp and alert is extremely important!
Yes, an officer is constantly in danger. You don't usually think about it, but, in the back of your mind, you know that any day could be your last. Instead you appreciate the teamwork and response time of your fellow officers. As far as scary calls, I had a few. But, I never got in a real fight ( a few scuffles, no fights) and I attribute that mostly to my philosophy of treating all people, including criminals, with respect, until they gave me a reason not to. Your training will see you through most situations. You will learn to act from training and instinct - police officers in hairy situations don't have time to think - their actions are not usually decisions as much as they are from training.
A "typical" day for me would involve some traffic control in front of the terminals - making drivers leave when they really want to sit and wait for their people. Responding to fire alarms, burglar alarms, or security breach alarms. Injured/ill persons calls, escorting ambulances to the aircraft door. Writing reports - if it's an arrest or possibility of getting sued, these need to be written very carefully! If on foot patrol, answer a lot of questions for airport patrons, or make small talk with them. Helping people find their car in the parking lot because they don't remember where they parked. Actual calls? Drunks, family disturbances, traffic accidents, pickpocketing, runaways, burglarized game machines.
In my 25 year career, I can recall 2 robberies, one stabbing, one accidental discharge of a firearm, two deaths (natural causes). Some narcotics cases, and some weapons charges, which usually came from the TSA at the security checkpoint.
With law enforcement, as with any career, there will be things that aren't as stimulating as you would like. It is up to you to find a way to fill the void. It could be through volunteer work - coaching, mentoring, etc, going back to school, taking up a hobby, etc. There are so many opportunities for advancement and specializing, it really does have something for everyone, and I encourage you to continue exploring it!
I hope this helps - let me know if you have further questions!