I cannot find a way of opening the right rear door used by catering vehicles. So I have the odd sight of a caterer walking through the closed door delivering food and drink.
This because your airplane doesn't have a proper configuration, because normally GSX is supposed to wait for a condition ( the door opened/closed ) before trying to have someone walking through the bulkheads. But in order to work, GSX must know this condition.
While this is easy enough to figure out on a default airplane, it might be more complex on a complex 3rd party add-on, that usually have custom variables to control their doors, so you will have to figure out the name of that variable, and write an ( easy ) XML expression to add the check.
Look the GSX manual at Page 28, there's an example of this, of course it must be adapted by the variable name used in the PMDG airplane.
I have used Shift+E followed by 3-9 but the door remains closed. Is there any way the door can be made to open?
An important note: GSX DOES NOT control your doors in any way. It only wants to *know* what variable is used to hold their current status, for the precise reason not having servicing people running through closed doors, but the actual operation of opening/closing a door, it's entirely outside the GSX control.
I don't remember how the PMDG 737 for FS9 was but, if it's similar to the FSX version, they control doors from the airplane FMC. The 747 used a menu with settable custom keyboard commands instead so, you might want to check the airplane documentation. In any case, having GSX installed or not, doesn't change in any way how you operate a door on any given airplane.