Yes.

When the manifolds are Haken this is a theorem of Waldhausen. See Ian Agol's answer here.

Since your manifolds are aspherical, they are irreducible by the Poincaré conjecture. Since they have boundary and are irreducible, they are Haken.

Yes.

When the manifolds are Haken this is a theorem of Waldhausen. See Ian Agol's answer here.

Since your manifolds are aspherical, they are irreducible by the Poincaré conjecture. Since they have boundary and are irreducible, they are Haken.