Speed control of DC motor
What you have described is a separately-excited motor, not a shunt motor. A shunt motor has the field connected in parallel to the armature while a separately excited motor has the armature and field connected to to two independent power supplies.

You are essentially correct in your description of the operation of the motor. The rating point of the motor is the point where the armature voltage and the field current/flux are at their maximum design points. Reducing the armature voltage below that point reduces the motor speed while maintaining a constant torque capacity. The power capacity reduces proportional to speed. Reducing the field current below that point increases the motor speed while reducing the torque capability at a rate that maintains a constant power capability.