Question

Electric field due to thin non conducting sheet of infinite extension

Answer 1

The answer is that the change in the component of the electric field that is perpendicular to the sheet of charge is:

n^⋅ΔE=σϵ0.

Specifically, n^ is the unit vector perpendicular to the sheet of surface charge. This is true no matter where the sheet is as long as it is smooth enough to be flat if you zoom in enough. In the case of the conductor you have a condition that the electric field inside of it is 0, so the electric field outside will be σ/ϵ0. With an isolated infinite sheet that is the only source of electric fields in the universe you have a symmetry that the field on either side has to have the same magnitude, even if the directions are opposite, giving |E|=σ2ϵ0.