No to one of your questions; here is an easy counterexample. Pick any base $B$ and let $A$ be a simple complex abelian variety then the pullback of $H^1(A,\mathbb{Q})$ to $B$ is a trivial, and therefore reducible, local system. But it admits no nontrivial sub variations of Hodge structure.
Added The newly added question is more interesting. Yes, if $V$ is a VHS which is irreducible as a local system, then $V_b$ is irreducible as a Hodge structure for very general $b$. This follows for example from prop 7.5 of Deligne, La conjecture de Weil pour les surfaces K3. It's probably also in Andre's paper that jmc referenced.