i.) to find the intersection with the z axis, set y=x=0; for y intersection, set x=z=0..and so on.
ii.) you have the function P = 6x + 3y + z - 6. Note that dV = dxdydz, so pick one (lets say dz) and integrate with respect to it to get integral(P, z) = 3xz + 3yz/2 + (z^2)/2 - 3z. Now, you do...