Question

charge Q has been spread uniformly over a circular arc of radius R and central angle 120°. What is the potential at the center of circle of the arc?

Answer 1

Whether it was spread or not is of no importance here. The whole charge lies at the distance R of the point where potential is required.
This should help you get to the conclusion.

Answer 2

yes - good point

Answer 3

this works for the center point, but does not work in ANY other point because there the distances are not equal

Answer 4

So being ignorant of the superposition integral of the potential (example is above) will prvent the solution in other points.

Answer 5

Definitely!