Cohomology of Solvable Groups

Question

The mathematician Morris W. Hirsch wrote on 1977 the paper "Flat Manifolds And The Cohomology of Groups". The Theorem C of his paper establish the following statement:

Let $G$ be a nilpotent group acting linearly on a finite dimensional vector space $M$. If $H^{0}(G,M)=0$, then $H^{n}(G,M)=0$ for all $n \geq 0$

My questions are:

1. Is this Theorem valid if $G$ is a solvable nonnilpotent group?

2. Is this Theorem valid if $M$ is a infinite dimensional vector space?