See the video of the dynamic model rocket launch.
From launch to Point A fuel is burning producing thrust. Where at point A the fuel is spent and thrust is reduced to zero.
From point A to point B the rocket coasts to maximum height.
From Point B to point C the rocket free falls.
At point C the parachute is ejected.
From point C to touch down the rocket descends with its parachute fully deployed.

1. What stage/s of the flight path are/is impacted by unbalanced forces?
From launch to point A unbalancec forces are acting on the rocket. This evident by the change in the speed of the rocket as it accelerates skyward. Thrust is greater than gravity and drag combined.
From point A to point B the rocket now is slowing down under the influence of gravity and drag forces. Unbalanced forces are acting on the rocket as it's speed is changing, slowing down.
From point B to point C the rocket is accelerating downwards. Since its speed is increasing unbalanced forces are acting.

2. What stage/s of the flight path are/is impacted by balanced forces?
Just before launch when the rocket is sitting on the launch pad, not changing speed, direction or shape.
When the parachute opens the rocket descends at constant speed.

3. What force/s are/is acting on the rocket as it remains on the ground after descending with its parachute?
Gravity is pushing down while the ground is pushing up with equal and opposite force.

4. What force is significantly changed when the parachute is deployed?
Drag.