What if 2 magnets repel one magnet? What happens if a singular magnet on a track is being repelled by 2 magnets on either side of the track? 
Will the middle magnet be equalized and sit still in the middle or will it continue to bounce back and fourth forever?
 A: 
Will the middle magnet be equalized and sit still in the middle or
  will it continue to bounce back and fourth forever?

The word "forever" is a red flag implying a possibility of a perpetuum mobile. So, just based on that, we can instantly conclude that, after bouncing back and forth a couple of times, the middle magnet will stop. 
The dynamics here are similar to a spring with a mass, where the restoring force is increasing with a distance from the neutral point.
A: If there is no energy dissipation mechanism and the magnet didn't start in equilibrium, it will oscillate forever. However, if it started in a position where it doesn't feel any net force or torque, it shall stay that way. 
A: Your example with the magnets is a good case to see if a pure magnetic interaction is a system without heat loses. Until now only in the idealization a process is reversible, no Perpetuum mobile is possible in reality.
In a first glance, if we have a pure magnetic interaction, excluding friction on the track, air drag, etc. (from the comment of @docscience), there are no other losses and the systems oscillates forever.
In a second view there are two phenomena, which prevent the system to be a closed system. The first is trivial; any accelerated subatomic particle emits photons and the emitted energy could come only from the kinetic energy of a moving system. Hence the kinetic energy decreases and the velocity of the oscillating magnetic goes to zero.
But an oscillating body with magnetic interaction has an additional source of EM radiation. To visualize these magnetic interactions we use magnetic field lines.

Source Wikipedia
They are closed for the repulsive magnets (see the sketch) and - the important point - they get deformed during the change in distance between the magnets. This deformations happens not only around the magnet, but inside the magnet too. Because of these deformations the subatomic particles of the magnet get displaced to each other (mechanical deformation) emit EM radiation.

Will the middle magnet be equalized and sit still in the middle or will it continue to bounce back and fourth forever?

Even if the middle magnet has an initially oscillation, due to energy losses from the accelerations and due to the mechanical deformations of the magnets, the magnets kinetic energy gets transformed into heat and the magnetic comes to stand still.
