Charges reside only on the surface of a conductor. Inside the conductor, charge is zero. So even, if the metallic cage was charge up with the help of powerful electric machine the charges resided on the surface. Therefore, we believe that Faraday was quite safe inside the cage.

Suppose the three charges be placed as shown in the figure.
      
As,the net force on q is zero, so it is already in equilibrium.For equilibrium of other two changes, the net force on charge Q at B is
\(\frac { 1 }{ 4\pi \varepsilon _{ 0 } } .\frac { Q_{ q } }{ x^{ 2 } } +\frac { 1 }{ 4\pi \varepsilon _{ 0 } } .\frac { Q.Q }{ (2x)^{ 2 } } =0\)
or
\(\frac { 1 }{ 4\pi \varepsilon _{ 0 } } .\frac { Q_{ q } }{ x^{ 2 } } =-\frac { 1 }{ 4\pi \varepsilon _{ 0 } } .\frac { Q^{ 2 } }{ 4x^{ 2 } } \)
\(\\ q=-\frac { Q }{ 4 } \)

Yes, the man will get an electric shock, if he touches the metal slab next morning because the steady discharging current in the atmosphere charges up the aluminum sheet. As a result, its voltage rises gradually. This rise in voltage depends on the capacitance of the capacitor formed by aluminum slab and ground.

Dielectric constant of water is much greater than that of mica because of the following reason
(i) water has a symmetrical shape as compared to mica
(ii) water has permanent dipole moment.

The insulating porcelain of the spark plugs accumulates a film of dirt.
The surface dirt is hygroscopic and picks up moisture from the air. Therefore, in humid weather, the insulating porcelain of the plugs becomes quasi-conductor.
This allows an appreciable proportion of the spark to leak across the surface of the plug instead of discharging across the gap.