Have upgraded my door locks and boot to a common key. They all work, and with the same key.
Can the locks be adjusted so that the passenger can lock the car with the inner handle as they get out, and then close the door, with it remaining locked? No need to use the key to lock it.
Like the passenger side on the early windup window models. Pull the knob up and close the door, and it remains locked.

Short answer is no, they can't. It's not an adjustment issue, but one of design. I think the theory being it not possible to lock the Keys in the Car.

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Yes they are physically designed to Prevent the door being shut and locked at the same time. It may be possible to modify but I have never tried

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1969 Cooper "S"
1967 Mini Deluxe
1973 Clubman Van (the fleet spare)
1978 ex 1275 LS ("Wizard" Eaton Supercharged)
2015 HSV GenF GTS(occasional drive & tow car)
2019 MINI F55 Cooper S

I guess that is why I have never locked the keys in the car. Thanks