Gauss's Law and Coaxial Cables

[tZimm]

The diagram I've attached shows a cross-section view of a very long straight metal cylinder of radius r1 within a coaxial hollow metal cylinder of inner radius r2 and outer radius r3. The inner cylinder has
a positive charge per unit length λ, whereas the outer cylinder has negative charge per unit length
-2λ. There are no other objects nearby.

So I know the field lines point radially outwards from the inner conductor to the outer conductor. But the following is what I am not sure with:
1. Why the field within each metal cylinder is zero during electrostatic equilibrium?
2. Why the electric field in the region outside of the outer conductor (region D) must be radially symmetrical and is this field equal in strength as the field in region B?
3. Using Gauss’s law to derive an expression for the electric field magnitude in regions B and D as a
function of the distance r from the center. The answer should be in terms of the linear charge
density, the relevant radii and the electrostatic constant. I have no no idea how to include linear charge density in this derivation.

Thanks in advance to whoever answers!

 

[cragar]

Is this a homework question?
on 3. How would I find charge in terms $\lambda$ and an arbitrary length of the cylinder.
We need to draw a cylinder in region B, how much charge is enclosed in my surface. What is the surface area in terms of the radius from the center and an arbitrary length of the cylinder.