Subject: electromagnetic interaction of charged particles - virtual photons

I have been thinking about how charged particles, say electrons,  interact with
 each other.  We know that they interact by exchanging photons and that this 
simple repetitive act, on a statistically large enough scale accounts for all 
the phenomena we see with the exception of nuclear and gravitational phenomena.
  if a light source emits light we can determine the frequency of those photons
 because either we stimulated the emission itself and we know how much energy we
put in, or because we can measure the wavelength directly.  But what if we 
consider electrons in isolation, interacting with each other.

If the universe was just a single electron then it wouldn't radiate at all. It
would not emit any photons. But suppose the universe consisted of just 2 
electrons seperated by a certain distance. 

We know that they would radiate only in the direction of each other because a
photon exchange is a 2-way process and an electron cannot radiate a photon 
unless there is another charged particle to receive it.  This exchange of 
photons accounts for the electrostatic force acting between the electrons and we
know it follows the inverse square law.
But what is the frequency of these photons?  And is the force between these 
electrons proportional to the number of photon exchanges per unit time, or 
proportional to the frequency of the photons being exchanged?
For example, if we move the electrons closer to each other so that the distance
between them has halved, then because the exchanges obey the inverse square law,
we know that the force acting between them will have quadrupled.  Does this mean
that they are now exchanging 4 times as many photons per unit time
or the same number per unit time but with 4 times the frequency,
one quarter the wavelength.
Surely there is a finite number of exchanges per unit time, surely these 
exchanges are not continuous. So how do the electrons know what wavelength of
photons to exchange? 
Doesn't this therefore mean that there is no such thing as a continuous force.
 That forces on the macroscopic level appear continuous because of a statistical averaging out of all these interactions.

If I push an object across my desk, the force is mediated by the electrons in 
the outer energy levels of the molecules on the surface of my hand, exchanging
 photons with the outer electrons on the surface of the object in question. But
 what is the frequency/wavelength of these photons being exchanged and why?

Re: electromagnetic interaction of charged particles - virtual photons