(a) Hint: If you draw an edge (link) from each node (n choices) to every other node (n - 1 choices), then you will draw every edge in the complete graph twice.
(b) Any tree with n nodes has n - 1 edges. By the way, it does not make sense to talk about a "minimal spanning tree" unless the graph has weights (or distances) assigned to edges. This is because any tree is minimal by definition: it ceases to be connected when any edge is removed. A spanning tree can be defined as a minimal set of edges that connect all vertices in a graph.