You've run out of the brake light fluid, need to get it filled up.
Actually the answer above this post is likely correct for your brake light issue.
HOWEVER, keep in mind only the marker lights in the tail lights flash on and off when you lock and unlock the car, not the brake lights, so that is not a valid test since you may be incorrectly assuming the those are the brake lights when they are just the marker lights.
the bulbs containing the brake light also contains the regular marker light, i.e. there are two filaments in the same bulb, so it's still possible that the brake light filaments of BOTH bulbs are burnt out, you need to rule that out by removing the bulbs and carefully examine to confirm both filaments are still intact.
If the high mounted 3rd brake light also does not work when you step on the brake pedal, AND you've checked to make sure its bulb is not burnt out, then yes it's the brake light switch above the brake pedal.
As for your lock/unlock issue, it can be a number of things again, it can be sticky/worn-out actuator which may need to be replaced, or could be sticky mechanism which needs to be cleaned and lubricated, only after opening up the panel to check will you know for sure.