STATEMENT(A): At the surface of a charged conductor, electrostatic field must be normal to the surface at every point                    

STATEMENT(B): A cavity inside a conductor is shielded from outside electrical influences.

Surface of a conductor has a constant potential. Therefore, there is no field along the surface of the conductor and hence the electrostatic field at the surface of a charged conductor should be Normal to the surface at every point.

Whatever be the charge and field configuration outside, any cavity in a conductor remains shielded from outside electric influence. The field inside a conductor is zero. This is known as electrostatic shielding.