Are carbocation intermediates in equilibrium?
Are the two carbocations in an equilibrium or are they formed in specific, fixed quantities?
  


$\ce{R-CH=CH2 + H^+ &lt;=&gt; R-CH2-CH2^+ + RCH^+-CH3 &lt;=&gt; alcohol~products}$

Yes, the two carbocations formed are in equilibrium. Initially the two carbocations will be formed in a ratio dependent upon the difference in activation energies leading to them (kinetic control).  However, since all of the steps in this reaction involve equilibria, after a while when equilibrium is established several things can happen


many carbocations will revert back to starting material which can then be reprotonated and reform the carbocations
or alcoholic product can be reprotonated, eliminate water and reform the carbocations
or the carbocations themselves can equilibrate directly by hydrogen shift


Once the equilibrium is established, the ratio of carbocations formed will be dependent upon the energy difference between the carbocations themselves (thermodynamic control).  Often, but not always, the relative stabilities of the transition states leading to the carbocations matches the relative stabilities of the carbocation intermediates themselves.


  
  If they are in equilibrium, i.e., the primary and secondary carbocation, why and how would the secondary carbocation revert back
  to being a less stable primary carbocation?
  


why - that's what happens in equibria; even though phenol is much, much more stable than its enol counterpart, there will be an exceedingly small amount of the enol present at equilibrium



how - by any of the 3 routes mentioned in the bullets above


  
  Also, is the hydride shift that converts the primary to a secondary carbocation the only shift that can occur; even if after the shift, a
  more stable carbocation can be formed (depending on the attached alkyl
  group)?
  


Other groups like alkyl or phenyl can shift too, but hydrogen shift is usually faster than the others.