the rear glass lock (when locked) prevents the button from being pushed in. if the lift-gate is locking on the remote and/or lock switch, then the actuator is working. perhaps the button is broken, or has become disconnected, on the window latch lock mechanism. you're going to need to remove the lift-gate interior trim panel and see what's happening (or more precisely, what's not happening) when you turn the key lock or lock button. Ford uses a lot of plastic clips on their lock rods. these clips often break or just come loose. their inexpensive (a few dollars) from Ford. that might be the problem or it might be something else. only way to know for sure is to check it out.
as far as the passenger side door lock... it could be a lack of lubrication problem or a broken wire in the driver's side door wire bundle. all 4 of my trucks required lock and latch lubrication to have the locks work reliably. does the door always try to unlock, or does it sometimes just act as if isn't getting power to the actuator? does it work always from the lock button on the passenger door? if it always activates the actuator it may be a lack of lube. remove the door panel and spray everything in that area of the door with WD40 and see of that helps. also check the lock knob to make sure the rod is straight and lube the knob too. if it doesn't always seem to send power to the actuator, it could be a broken wire in the driver's side door wire bundle. to check, take apart the black plastic cylinder (remove center plastic cap and 10mm bolt) and look for any for broken wires.
lastly, sometimes the actuators just wear out and aren't strong enough to unlock the door, sometimes they need to be cleaned out and re-lubed internally (they're not designed to be taken apart, but it can be done by drilling out the case. afterwards you'll need to add a couple of small screws to hold the case together). sometimes the rivet that holds the actuator to the door can come loose and cause the actuator to not work reliably, or at all. good luck.
