All points on the circumference are equidistant from the circle's center true or false

That would serve as a definition of a circle. It is like asking if all radii of a circle are equal. Both statements are true. A radius is a line segment joining the center with the circumference. All radii are equal.

All the points of a circle live on a locus that is equidistant from the center. You can count on death taxes and any point on the circumference of the circle as being equidistant from the center.

True. No exceptions.