Why induction coupled plasma use RF frequencies? The frequency I see all the time is 13.56mhz,I understand that when you want to make heat treatment surface finish on steel,you use high frequency in the heating coil so the skin effect heats only the surface,but I have no idea why it would be frequency of choice for turning gases like argon into plasma.
Why people use 13mhz to turn gases into plasma? What effect does the frequency have in this process? What would happen if we lower or increase the frequency in the coil?  Does 13mhz somehow turn the gas into plasma faster or more efficiently? 
 A: Some ICP systems do use lower frequencies, down to about 500 Khz - and I recall seeing some systems operating in the sub-100 KHz range. In fact, lower-frequency drivers have a few advantages; the paper

Xu, S., et al. "Low-frequency, high-density, inductively coupled
  plasma sources: Operation and applications." Physics of Plasmas 8.5
  (2001): 2549-2557.

has a good introduction to the effects of different exciter frequencies.
Miniature ICP systems running at 50+ MHz are also seen in the literature.
Insofar as I've seen, the main rationale for 13.56 MHz specifically boils down to availability of off-the-shelf high-power generators and matching networks  in the ISM bands. 
2.4 GHz plasmas are also common; plasma lamps are a striking (ha!) example of this. This seems to come down to a matter of terminology; microwave coupling effects behave somewhat differently than a simple LC-tank, so "RF-excited" makes a bit more sense than "inductively-coupled".
I don't know nearly enough plasma physics to say why 13.56 MHz is more common than 27 MHz, however.
60Hz plasmas aren't really possible, as you need the electric field induced by the alternating magnetic field to be sufficient to ionize the gas. 
The book Fundamentals of Electric Propulsion (pdf warning) discusses this at length in section 4.5.
A: Plasma frequency is the natural frequency a plasma's density changes at on the mesoscale.
I believe that this intro to fusion tech gives a good explanation of the plasma frequency in the first chapter, but a relevant wiki article is plasma oscillations. The equations look like they give frequencies matching the one you described (presumably megahertz, not milli?) 
