Why must electrostatic field be normal to the surface at every point of a charged conductor ?

Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.

Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?

A conductor with respectivity rho bounds on a dielectric with permittivity epsilon . At a certain point A at the conductor's surface the electric displacement equals D the vector D being directed away from the conductor and forming an angle alpha with the normal of the surface. Find the surface density of charges on the conductor at the point A and the current density in the conductor in the vicinitity of the same point.

Why should electrostatic field be zero inside a conductor ?

Why should electrostatic field be zero inside a conductor ?

Why are electric field lines perpendicular at a point on an equipotential surface of a conductor ?