if i had to make one guess that connected most of those symptoms together, i'd say the battery is weak.. internally weak due to age or or partially discharged or not able to hold a full charge for some reason... maybe just corroded connections or a weak ground between battery negative and the engine block..
If so, when the accessories demand power, the battery alone cannot supply all that is demanded.. At that time, current is drawn from the magneto. A large, steady load on the magneto absorbs a greater amount of engine power.. If at idle, the engine could die. The draining effect would exist at high RPM too but might be less obvious.
As far as why accessories get any current at all without the battery, i dunno.. My guess is as you say .. there's some quasi-connection between ignition and accessory power.. perhaps through a large resistance of some sort. Determining exactly what it is would require studying that wiring diagram you mentioned..