Has anyone had a fender burst from being put under too much pressure during a storm etc?
Yes, and I’ve seen it happen to other boats numerous times.
Yes but the more likely scenario is that the fender will break loose before it pops. Part a line etc
If you don’t want any fenders bursting take some mooring line out of service and make one that can’t burst. I use a square braid. But that’s just me being presumptuous. To answer your question, yes I’ve seen fenders popped under heavy loads.
There’s not a yachtie in this world that would hang a rope fender like that over the side!!
Depends on the condition of the line but I’d say there are plenty of yachties who would do that. You’re right in that you won’t see a rope fender hanging anywhere near chrome and tinted plexiglass but a woodenboater would use a rope fender in a heartbeat.