2005 expedition and all door locks and remote not working, idk if related but door ajar light is on on dash and radio don't turn off when key is off and door opens.

Do you have a door ajar light on in the dash?

Try getting out of the car, close the door, lock it with the remote.
Then, open the door using the KEY and try to start the car.

You probably have a broken door switch., so the system thinks a door is open. Fairly common failure, easy and inexpensive to fix.

This is not a good thing. Ford uses a computer called the GEM and that means General Electronics Module. It controls:

• Low Coolant Indicator On Cluster
• Brake Indicator on Cluster
• DRL - Control
• Wipers
• AutoLamps
• Rear Defrost
• Interior Lamps(dome)
• High Beam Indicator only (cluster)
• Low Coolant indicator
• Key-in Buzzer
• Seatbelt indicator only (Cluster)
• Trunk Pop Relay
• Power Locks
• Door Ajar Sensors
• Door Keyless entry pad
• Remote Keyless Entry
• One Touch Down (power window)
• Air Bag Tone
• Anti Theft (perimeter Alarm) (SEL, or SE(s) with mods)
• Lift gate ajar (wagon)
• Liftgate Pop
• Accessory Delay signal (accessory that work after engine off, prior to door ajar)
• Battery Saver Relay signal (accessory that work after engine off, 15 mins) Map lights, vanity mirrors

They are located behind the radio in the dash and they are $$$ about 600 USD.

This may be because the door control computer does not see all the doors locked or closed all the way, make sure the doors are all closed completely and the door ajar light on the dash is off, If this is not the problem then the door control computer or the body ECU may be faulty.

check all door switchs the most comun is the driver side maybe is fail or disconected and fuses too,

Your keyless entry system is going bad and you need a battery for your keyless entry system once you replace your battery with the new one thing should work properly

Check your door latches. Since the light stays on, one of them isn't reading properly. Once you get that fixed, the remote should work. The light problem could be related. The computer thinks the door isn't shut so that part of the system thinks you aren't moving.

At least one of your door ajar switches are sticking. If you have tried lubing them,then the switch needs to be replaced. This is causing most of your concerns. Try one door at a time to see if the light goes off. The most common switch is the driver's door.Good luck.

You have a wiring harness problem
Take it to the dealer directly.......