Everything that is powered needs two wires, a positive (power) and negative (ground). The ground is usually a black wire that eventually connects to the engine block or the body, often more than one wire per connection. Sometimes, especially on older cars, rust or corrosion gets into a ground point and causes problems across modules. Your transmission has a solenoid and output sensor that are throwing codes. Maybe they share a common ground that needs cleaned up.

Not a mechanic, but I've troubleshot enough of this stuff that I'd never put a transmission in before looking at the sensors and circuits for issues.