Research reveals that the error code 02 is a common one, and that Mamiya error codes don't reveal much detail. Advice ranges from reinserting batteries and checking they are charged, to making sure to turn on the digital back previously. However, as the other lenses work, it is clearly not user error.

I found that the protocol between the camera and the back is based on SPI (source). As the camera back and the lens mount have the same number of pins, it is not unreasonable to assume that they didn't mix-and-match protocols.

If you have an logic analyzer or similar on hand, you could capture and analyse the communication between the camera and the lens. However, this likely won't give you much more additional information though - the error code 02 is likely an unspecified lens error or similar. If you do decide to try this route, the easiest thing is to get a lens adapter or teleconverter, partially disassembling (depending on product) and then solder wires to that rather than attempting to use alligator pins on the camera's pogo pins. While you could use an Arduino for this, I strongly recommend against it and would suggest using a USB logic analyzer instead.

It's most likely the aperture, due to two reasons - the camera shop's notice, and the fact that the sound happens when pressing the depth of field preview button. You could verify this by holding the depth of field preview button while changing the aperture.

The most reasonable advice would be to try to get your money back for the lens. Failing that, you could attempt to take the lens apart and check if the mechanics or something appear to be damaged. I do not recommend this though, as reassembly can be difficult, the odds of actually finding the issue is low for the untrained eye and you are likely to introduce dust or other foreign objects into the lens.