False. "All net forces" are toward the center in this case, which is not at all the same as "all forces".All forces are toward the centre, including the force on the person causing holding the other end of the rope.
The F in that equation is the net force.I was distinguishing tensions from forces (F=ma).
This is nonsense. A third law pair act on different objects and they are never summed to determine a second law net force or acceleration.If the forces on the rope and the the stone were equal and opposite there would be no acceleration, which is not the case.
You should stick with this objection. Your technical objections are flat out wrong. If you don't like a term then you don't need to use it. If it causes confusion or is redundant or has other semantic problems then explain that. But like it or not the term is well defined and the concept has no technical deficiencies. The only possible objections are semantics and personal preferences.I suggest that "centrifugal" should not be used to describe the 3rd law pair to the force on the stone. In my view, it simply adds confusion