(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}