Suppose electric field inside the sphere is nonzero. Then since there is no charge inside the sphere and since electric lines of force do not form closed loops so we should be able to find two points A and B on the surface of sphere such that a line of force starts from A and ends at B, thus causing a potential difference between these points. But since the sphere is made of metal (which are usually good conductors) so there will be a flow of current between these two points until the potential difference between them vanishes. So in equilibrium i.e. when no current is flowing, electric field inside sphere should be zero.
When lightning strikes a car, it is not simply charge separation that protects the occupants; the conductive skin provides a preferential path for a current. If the charge were to simply be deposited on the skin of the car, something exciting might happen, but in fact the charge is carried through the car to the ground. It is definitely possible to apply a large enough current that ordinary conduction no longer occurs, but this isn't because the metal skin runs out of electron/hole pairs -- it's because the skin heats up and vaporizes!
Your premise for part 2 isn't quite correct. If you stick an electron inside a neutral, conductive sphere, you can still see the charge outside the sphere. If the sphere is grounded, then you will not, but that's because you've essentially hidden the charge on the ground and given the sphere an opposing charge.
Conductive shells shield their contents from external fields, but they do not shield the external environment from the charges of their contents.
If you add charge, grounding will continue to cancel your fields. If you increase the charge rapidly, then you can gain a momentary field, but currents will eventually cancel the charge accumulation. (Essentially, you are charging a capacitor, which is leaky because of connection to the ground.)
To return to the question you posed in part 1; what happens if we apply a slowly increasing field to a hollow conductive sphere that is perfectly insulated from ground? At first, polarization will shield the interior of the sphere from the external electric field. The conduction electrons will flow to create a polarization across the sphere. Eventually, however, the material will breakdown.
Exactly how is a matter of conjecture, on my part. Because the sphere will polarize, with electrons accumulating on one side and bare ion lattice on the other, I hypothesize that the ends of the sphere will begin to smear out perpendicular to the electric field. The electric field balances the repulsion between like species along the electric field, but not across it. Therefore, the ends of the sphere will experience a shear that thins them and breaks them. These broken pieces, being charged, then fly along the electric field at colossal speeds, allowing electric field into the erstwhile interior, and badly damaging your lab.
Best Answer
The field inside the sphere will not be zero if it is hollow and there is a point charge in the hollowed out part. The field will be zero in the conductor, because the field is always zero in a conductor in electrostatics. What you might be refering to is that the field will be zero inside the hollow sphere if it is charged, because the charges will distribute symmetrically over the sphere.