Polaris
Circumpolar stars/constellations always stay above our horizon, if they go below our horizon than they are no longer circumpolar.
At the North Pole, and at the South Pole.
Subtract your latitude from 90° and that will give the the decollation of circumpolar stars. In northern New Zealand, my latitude is 35°. If I subtract that from 90°, I get 55°. So stars with Declination great than 55° are circumpolar for me.
Circumpolar Constellation
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?
They are always visible in the sky. (Unless it's cloudy). They don't "rise" and "set" at the latitudes where they are circumpolar.
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.
No they do not. By definition circumpolar stars do not "rise". They are above the observer's horizon at all times.
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.