Sorry for delayed response, got caught up at work and thank you for clearing the problem statement.
The service of the electric motor will be of the intermittent type
That's good !! Easier of the 2 cases.
What do you mean when you talk about balanced / unbalanced system?
You need not worry about balancing WP system, that was for Dynamic analysis Case 1.
Also in the second case, that of intermittent rotation with 90 ┬░ angles, should I still carry out a fatigue analysis of the PS system? Or would the effect of fatigue be negligible in this case?
I do think Fatigue analysis is not required even though the PS system will be in alternate tension and compression in 360┬░cycle (at least not initially).
Yes, the angular rotations are fixed, and even I actually thought of considering the most disadvantaged case the one with static load at 90 ┬░ (i.e. when the moment arm is at its maximum)
Doing 1 case is not sufficient is what I think, because the PS system is going to be in tension and compression alternately, thus I was wondering if we could solve this problem in 4 steps with CG of the WP (along with PS system) changing its location by 90┬░ rotation in every step.
I have a question about this simplification of the problem. If I eliminate the point mass, how can I then insert the centrifugal force in the model?
So for intermittent rotation we can consider your problem statement under static loading and no need to consider centrifugal force effect (I am assuming the angular velocity is very low thus high torque).
I also have a practical question. When do you say that I have to add the moment at the WP end of the shaft, at what point of the shaft are you referring to in particular? In other words, which area should I select as the area of application of the moment? The more external surface of the shaft / flange?
The highlighted are is where the WP shaft fits right ? That's where that shaft will apply moment (Force) on PS system.

Also what I would have done is considered WP shaft, then PS system, turret and linear actuators simultaneously with WP shaft, Linear actuators as Rigid bodies while everything else as flexible body with BC's as Fixed support at Actuator base, Pin fixed to Top of Turret (I saw that there are bearings housings which are mounted on top of the turret) and so on if you are interested because then you would directly get stresses developed in Turrets and load at the actuator base. Also I think there should be ribs supporting the turret and minimize the tilt avoiding slippage of shaft from PS system.
I have another question, is the design of Pin confirmed and cannot be changed ? I was thinking about it last night and I thought a squared shape pin (and not tapered) with a considerable entry chamfer at the WP end of shaft would make a better pin design, avoiding slipping, reducing tilting of Turrets and increasing overall strength of this structure. (if the diameter of pin is more than 25mm then we can go for hexagonal shaped pin too)
Thanks Chinmay