Question about the locks/FOB

Interesting! I've never tried opening the door after seeing/hearing the door lock, even after pressing the button once and not setting the alarm. Have you replaced the battery in the fob? Perhaps it is dying and not functioning properly

Arming the System
When armed, the perimeter alarm system is designed to notify the driver of an unauthorized entry. When unauthorized entry or towing occurs, the system flashes the turn signal lamps and interior lamps and sounds the anti-theft alarm and the traffic horns. The system is ready to arm whenever the key is out of the ignition. Any of the following actions arm the alarm system:

Pressing the RKE transmitter lock control 1 time to arm the system.
Locking all the doors using the door lock control switch while the driver or passenger door is open and then closed.
Locking the driver door with the key in the driver door lock cylinder (this does not arm the interior motion or vehicle inclination sensing systems).
If all the closures (doors, luggage compartment lid, and hood) are closed, the turn signal lamps flash once. If the vehicle is locked again within 3 seconds, the vehicle locks again, the turn signal lamps flash and the horn chirps. If any closure is not properly closed, the turn signal lamps do not flash and the horn chirps twice. The system waits 20 seconds after locking before triggering an alarm. After the 20 second pre-arm phase, the door lock control switch is disabled (if door lock inhibit function is configured on) to further protect the vehicle.

NOTE: Deactivating a sounding alarm by pressing the PANIC button on the RKE transmitter returns the system to an armed state.

NOTE: Unlocking the luggage compartment inhibits the interior motion and inclination sensing systems, but the perimeter alarm system continues to monitor the doors and hood. Once the luggage compartment lid is closed the interior motion sensing systems are again monitored.