Electric field inside and outside a hollow spherical shell If a charge(+q) is placed at distance away from a hollow spherical conducting shell , would the net electric field inside the hollow portion remain zero? If the +q charge was placed anywhere inside the hollow 
portion , would the net electric field outside the hollow sphere be zero?
 A: If the charge is outside the hollow spherical conducting shell, the field inside the shell will be zero. The shell (or a closed conducting shell with a random form) will shield the field. The shell acts like a Faraday cage.
If the charge is inside the shell the field outside the shell will be the same as if there were no shell at all.
A: 
would the net electric field inside the hollow portion remain zero? 

The answer is yes, spherical or not spherical. The reason is that the
bulk of the conducting shell is equipotential and as a consequence in
any point within the cavity potential is also the same, then 
$\vec E=0$.

If the +q charge was placed anywhere inside the hollow portion,
  would the net electric field outside the hollow sphere be zero?

No. You find a total charge $+q$ distributed on the outer surface of
the shell (and a charge $-q$ on the inner surface). If the outer
surface is spherical the external field is the same as that due to a
charge $+q$ placed in the centre. Note that this remains true
whatever the position of internal charge.
The reason is that the external surface is equipotential, and by
symmetry the external field is purely radial and only depending on
distance from centre. Then apply Gauss' law.
