Hi, regarding your first question:
The electric fields coming out of a charged point particle or
charged sphere can be resolved in two directions, as they are
vectors. Perpendicular to surface, and tangential to surface. It is
analogous to how projectile motion can be analyzed with respect to
a X, and a Y direction.
The component in the tangential direction must be zero because
there cannot be a force between two equipotential points. Therefore
the electric field must be perpendicular..
I hope I'm right!