Re: Has an escape velocity and/or force been established for an electon?

Your questions are oddly phrased, but I think I understand what you are
asking.  There are simple (and not-so-simple) answers to your questions,
but I'll try to explain what these answers mean as I go along.

First, about the 'force' required to pull one object away from another: 
this is more properly described as an amount of work, which is to say the
integral   of the applied force along the direction in space that the force
acts (or, to put it loosely, the average applied force multiplied by the
distance over which the force acts).  In the two cases of interest, the
gravitational and electrical forces, the minimum amount of work required
can be calculated from a simple formula.

In the case of gravity, this minimum amount of work can be re-expressed in
terms of a velocity (assuming that the two objects are at rest with respect
to each other initially), and this velocity is called the 'escape
velocity'.  For a small-mass object escaping from the surface of a
spherical body (such as a planet) with mass M and radius R, the escape
velocity is the square root of 2*G*M/R, where G is the universal
gravitational constant.

In the case of a hydrogen atom, things are different, because the proper
description of what happens is given by Quantum Mechanics.  The energy
required to strip the proton of its electron can be easily calculated, and
also very easily confirmed experimentally:  13.596 electron-Volts, or
2.1784e-18 Joules in SI units.

Making an equivalence between gravity in planetary systems and electric
forces in an atom is tough, because the fundamental description of what's
happening is so different: classical physics in the case of planets
(loosely speaking, again) and quantum physics in the case of atoms.  It's
difficult to determine what you mean by 'the same relative mass and
distance as the electron', or by comparing a planet to an electron 'if the
proton was the size of the sun'.  You might get some mileage comparing
planetary systems with the Bohr model of the atom, but I'm not sure that
this is exactly what you had in mind.

In any case, I think you would be well-served by reading any calculus-based
high-school or college physics textbook, especially those sections relating
to Work and Energy, Gravitation and The Electric Force.  You should also
read any sections on so-called 'modern physics', including the Bohr model
and some basic quantum physics for the hydrogen atom.

Good luck, and if you have any more questions feel free to ask!