Can a bluetooth device open an app? Can a bluetooth device, like a panic button, launch an app when pressed and have the app call a pre-programmed number or does the app have to be running for it to be accessed by the device?
iOS apps are allowed to monitor for specific Bluetooth LE(Low Energy)/4.0 device services in the background.  But not regular (non-LE/4.x) Bluetooth devices.

However, iOS apps are not allowed to start a cellular phone call without specific user interaction (for obvious security reasons).