If the total charge enclosed by a surface is zero does it imply that the electric field everywhere on the surface is zero, conversely, if the electric field everywhere on the surface is zero ? Does it imply the net charge inside is zero ?

Explanation

No, since `ointE*dS=(q)/(epsilon_(0))=0` therefore the field may be normal to the surface.
However, the converse is true, i.e. when `E=0` everywhere on the surface, the net charge inside is zero.