(1) The graph is K_2 x K_3.  The number of spanning trees is 75.

(2) The resistance is 2/3.

(3) The chromatic polynomial is t(t-1)(t-2)^4.
The chromatic number is 3.
The number of acyclic orientations is 2*3^4

(4) (a)  m n^{n-m-1}
    (b)  n_1 ... n_k (n_1 + ... + n_k)^{k-2}