Most of those are not relevant to emergencies. They are either a normal part of everyday flying where I would often use an autopilot, but mostly not relevant at all to BN-2 operations.
Heavy ATC workload is normal in southe-east England, but it is remarkable how it suddenly clears with the words "Mayday, Mayday, Mayday", if you are considering an emergency situation.
Sudden changes of routing are part of my daily work, although less so for the short-hop scheduled boys. They also seem to give multi-crew as much trouble as any pilot I would sign a line check on if the radio is anything to go by. If necessary direction can be requested from ATC, and they are sympathetic when reminded we are single-crew. Good CRM.
Flying complicated vertical and horizontal routes is again routine in England. Nothing special, just keep the plog up-to-date and if given an unexpected waypoint ask for vectors (as I have heard multi-crew pilots with full FMS do!). Hard work, but hardly an emergency.
Sick and distressed passengers cannot easily be helped on a short route more than being landed ASAP. Emergency call if necessary, but autopilot no help.
Oxygen pipes in an Islander? Have you
seen one? Does it look like it is worth flying above FL100, remembering that unlike me it doesn't even have turbo-charged engines?
Having a wee and 7-hour legs fall to the same objection: not only can no BN2 fly long enough to require this (even our longest-range aircraft cannot fly for 7 hours with reserves for public transport) it is never used for long legs, as no-one would get on one again after experiencing more than 45 minutes in one. Oh, and last time I had to have a wee in the air I had to fly the aircraft, due to turbulence.
I am not saying that a high workload is more safe. I am saying that in some circumstances the pilot should be flying the aircraft, so he knows what is happening to it. I never said APs were a liability, I said I will usually use one, I simply said that the reason I do is not to do with emergencies, and in many emergencies (I would include anything that affects handling, including an engine failure) I would want to be flying the aircraft until I have stabilised the situation. In the case of a BN2 I would be pretty much on the ground by then: they don't go far from the nearest suitable.