If a non-unit-speed has constant curvature and zero torsion, is it a circle necessarily? I've found an answer to the question I had here. But in that answer, we assume that the curve at hand has unit speed. In working with the cross-sectional curve of a circular helix, I do not know my curve has unit speed. How can I still show that the cross-sectional curve is a circle? I have demonstrated that it has constant curvature, lies in a plane and has zero torsion.

The shape of the trajectory does not depend on the speed, so it needn't be unit. (Think that tough you can drive at different speeds, the road remains unchanged. :)

The curvature and torsion formulas are established by computing the curvilinear abscissa, which "normalizes the speed away".