For #2, I think the device is just a wire running from the ignition switch to the isolator selenoid.
The isolator probably has two heavy wires and one light control wire. Look for a voltage on the control wire when the ignition is turned on. If it isn't there, you could just connect it to something else that powers up when the engine runs. Or replace the isolator with a solid state one that doesn't need a control signal, just passing current when the higher alternator voltage appears on the heavy wire. Of course a problem with the ignition switch might be causing the other problems, too. I once fixed an ignition switch by squirting it with electrical cleaner.
2004 E350 Adventurer (Canadian) 20 footer - Alberta, Canada
No TV + 100W solar = no generator needed