Just to be clear, the results for constant circular motion mentioned here:

1. "none of the actual velocities going round the circle are zero,

the total sum of all the velocities will be zero."

2. "The average velocity will be 0 but the velocity at any time is not. Also, the average speed is not 0."

Assumes that you are considering a single period*, where the object travels around the circle back to its start point. If you're not considering a single period, let us know because things can get a little bit more tricky.

*actually \(\displaystyle n\) periods of circular motion, where n is a positive non-zero integer.