Yes, given the age I expect its wired carplay and not wireless.
As an overview, Apple carplay requires an approved interface chip and sign off by Apple in order to support the functionality, however Apple then screw up the interface at every update

I would always advise avoiding Crapple updates for the first 4-6 weeks.....
As for the cables, the dealer is actually correct, the data loading Carplay (and Android Auto, Bidu etc) put on the system means you need a decent cable and not just the cheap tat which people only use for charging, long cables can also create issues.
Unfortunately the system in the Pugs is running on the edge and the software gets chopped and 'optimised' just to get it working so can be a bit flaky (hence why you might see a fresh 'oh shit' release shortly after you get an update)......it doesn't help that they don't have Software Over The Air (SOTA) working either.
We see loads of customer complaints following Phone updates..........the car has not changed, the phone has yet its the cars fault (happens on Android to but, much less often and not on Android Auto, not seen an issue for over 12 months and that was only on our older systems as they moved to a new Bluetooth stack and 'forgot' to enable backward compatibility).
I should add, it does sound like there is a more fundamental issue given the audio distortion, pretty much every system these days has a DSP audio processing stage to support cabin audio tuning, echo cancellation (voice calls) etc, it sounds like this is not loading correctly......as for the system crashing, this also points to a software install issue. The trouble is the dealer wont actually be able to do a full fresh software install so would be a head unit swap out (If it was me I would be looking to re-load the audio config files......but the dealers might not have this ability)