Electrical mystery--set out to fix 2 problems but fixed 3

You're way too deep into electrical to not be using a meter. Those 3 light testers are handy for quick checks but will often confuse things as you have discovered. Get a proper volt meter and check for voltage you have: Hot - neutral, hot-ground, neutral-ground.
Did you ever plug in any of these 3 light testers before when running on generator? If not then you don't know if it's any different now or not.