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.

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 André's paper that jmc referenced [it's lemma 4 in André, I just checked].

No to the last question, 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.

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.