Hi BG
You have perfectly represented the trichotomy of man.
I would like to add this:
The Spirit is our "God part".
The soul is what makes us be us. When I was Learning the above, it was said that even animals have souls. This is why each dog is different and each cat is different, as we could note if we have had pets.
But, yes, indeed the soul is affected by the spirit.
Even the body could be affected by the spirit.
Studies have shown that patients that pray have a better chance of a cure than those that don't.
I couldn't find an image like you explained, which I agree with, but I did find this: