On a microscopic scale, yes it is the electrons repelling each other-" everyday " electrostatic repulsion ( for instance, rubbing a balloon on your hair ) might not look like much, but the force varies as 1 / r 2.
2.
I attempted to work out the position, velocity, and acceleration as functions of time for two electrons repelling themselves, but I got stuck when it boiled down to z / x ( t ) ^ 2 = a ( t ), where z is a constant, x ( t ) is position, and a ( t ) is acceleration of x ( t ).