1). It keeps running
2). Yep, there's that annoying beep that you have to stop the APC cook to clear.
It's for this reason that most of us don't use the timer in the app. Me, I use my calendar in my phone for longer cooks - any timer in your phone will also work just as well.
You really wouldn't want the APC stopping the cook at the end of the timer - if you're away / asleep, your vessel could cool off and put your food into the danger zone (40F-129F) long enough to make it unsafe.