Voronoi diagram with given number of vertices and sites
Conceptually, it is maybe easier to construct a Delaunay triangulation tessalation. The DT is the dual to the Voronoi diagramm, so you want to limit the number of faces to $0,1,4,7$. This can be achieved by placing some of the vertices of the DT on a circle, or by picking the right number of vertices on the convex hull.

Here is a picture for the 4 vertex case (black DT, red Voronoi diagramm). Play around to get the solutions of 2. and 4. (You already solved 1.)