Suppose the monkey is applying a force F on the rope. So it in return feels the reaction force F towards the ceiling. Tension also develops here in the rope as well due to the force F and it is equal to F.
Now we know that the rope will pull the monkey up with tension force. so the monkey feels F upwards. But the monkey at the beginning also experiencing force F from the 3rd law reaction. So is it that the monkey applying a force of F downward will feel a force 2F upwards in return.
Now bringing friction into the play. When the monkey pulls down the friction pulls up.Let the friction be f. now the rope also feels a force of f. It means that the final tension should increase and become F+f. So the monkey will now feel an upward tension of F+f.
So eventually we have a monkey applying a force of F on a rope and getting 2F+f force in return.(one F from 3rd law reaction when it applied a force F in the first place. Another F+f from the tension in the rope.
So where am I wrong here ?