As long as the moving pulley is taken as the analysis object, the force analysis is carried out. All the problems are almost solved. Like the last picture. The friction of A is F, and the tension of the rope is obviously equal to F. For the moving pulley, the tension of the two ropes is left. The resultant force is 2f, the pulling force to the right is f, and when moving at a uniform speed, F=2f.
As for the distance, the mathematical relationship. It may also be explained by the principle of hard work.