Good clarification, da Rock!

Static thrust means the prop's baldes are working at the max AOA.

Once the plane start moving forward, the AOA gets smaller until reaching a min at top forward speed.

This happens because the air hits the prop at a smaller angle when the plane is moving.

No, the plane of reference is not relevant, since force is force, whatever the direction is that it is applied towards.

Gravity is just a force, which we call weight.