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These are all functions of the central locking system.
This year/model is susceptible to water intrusion into the Central Locking / Anti-theft control module. I recommend you go into the trunk remove the panels or trim to access the right rear corner below the right tail light assembly. There you should find the control module. Inspect for water and or corrosion on the electrical connecters. Typically what happens is the seal at the taillight fails (previous collision?) and water gets in. If this is the case you may have luck taking the controller apart, drying it, and cleaning the electrical contacts. If it has been like this for awhile you may need to replace the unit. Be sure and water test the trunk before returning the vehicle to service.
If you do not find water intrusion to be the cause of your concerns, the controller's on board diagnostics should be scanned for trouble codes and the diagnosis would proceed as indicated by the trouble code(s) retrieved. I would normally do this as part of my initial inspection, but realize you likely do not possess a capable scanner to access the system.
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