You're about right. I will add this: Rake determines the "steering speed" and trail is the steering's tendency to "self correct".
Increasing rake (numerical degrees, that is) make sthe bike steer slower. Decreasing rake makes the bike steer faster. Increasing trail makes the bike more stable and track better (like when you let go of the bars, the bike won't wander). Decreasing trail makes the bike less stable and track more difficult.
Your 4 complications are dead on and broken down so nicely it's perfect. Additionally, tire profile and width will affect stability, steering and rider input too, but that has nothing to do with rake and trail.
--The Fox