Hermite curves are very easy to calculate but also very powerful. They are used to smoothly interpolate between key-points (like object movement in keyframe animation or camera control).
http://cubic.org/docs/hermite.htm
In general, a Bezier curve section can be fitted to any number of control points.
The number of control points to be approximated and their relative position determine
the degree of the Bezier polynomial.
Another important property of any Bezier curve is that it lies within the convex hull (convex polygon boundary) of the control points. This follows from the properties of Bezier blending functions: They are all positive and their sum is always 1
So, I, II, III are true