As someone who learned the trade installing conduit systems (even in residential), this is an excellent example why those of us who do electrical installations with conduit think romex is a joke. Yet the majority of residences in the US are wired with what is essentially extension cords. I don't care what the NEC says, romex is a joke.
Had this installation been done in conduit, there would have been color-coded wires that would have been easily identified. With conduit, you don't see white wires used as current-carrying conductors. You don't see a white and a black and a red terminated together. And a whole bunch of other things that I, and pretty much every electrician I've ever worked with, consider flat out wrong and potentially dangerous.
Mike, I have said before here that a woodworker's forum is not the place to ask for electrical help. But even if you go to Mike Holt's website and get some good advice from the electricians who populate the forum, you still may not understand the little inner workings of how electricity does what it does and what actually works and what doesn't. Even inspectors don't take the time to check to make sure everything is done right, and some don't even know what to look for.
I suggest you hire a qualified electrician to give you and your family some peace of mind.
“Travel is fatal to prejudice, bigotry, and narrow-mindedness..." - Mark Twain