minimum number of points a convex hull must have
The convex hull of 10 collinear points is the line segment between the two extreme points.
No, a convex hull does not have to be convex polygon. A convex hull can be a point, a line segment, a ray, a line, a convex polygon, a circular sector, a half plane, a cubic, etc. .
A definition in math, such as the definition of convex hull, is the strictest kind of definition. It means exactly what it says. No more, no less.