They are always visible in the sky. (Unless it's cloudy).
They don't "rise" and "set" at the latitudes where they are circumpolar.
All stars are circumpolar
At the equator, you will see no circumpolar stars.
A circumpolar star never sets below your horizon.
Circumpolar motion refers to the motion of the stars relative to the viewer in a particular spot. Stars that are said to be circumpolar never cross the horizon as they cross the sky for the viewer.
If you were standing on the equator, how many circumpolar stars would you see?
(circumpolar - our view of the constellation on Earth) Constellations are circumpolar because they are only how we view them on Earth. The constellations would be different on another planet or at another viewing point. They are circumpolar since they are at different distances in relation to each other and to the Earth.
During roughly half of the time, 'circumpolar' stars don't appear to move from east to west. Which ones those are depends on your latitude. All other stars all the time, and circumpolar stars for the other half of the time, do appear to move from east to west.
No. The Zodiac are 12 constellations that lie in the plane of the ecliptic; circumpolar ("moving around the pole") stars are well above or below the ecliptic.
Polaris
Circumpolar stars/constellations always stay above our horizon, if they go below our horizon than they are no longer circumpolar.
For example, if you live at a latitude of 50° north, the circumpolar stars will be all stars that are up to 50° around the celestial north pole. As another example, if you live at a latitude 30° south of the equator, the circumpolar stars will be all those that are in a circle up to 30° around the celestial south pole.
At the North Pole, and at the South Pole.