What happens to forces when a charge travels at near c? Suppose 3 electrons are travelling at $c - 1$mm at 1 cm distance

The charges are at rest relative to one another in their frame, but what happens to fundamental forces Fe and Fg? What Fe does A get from B or C? and what about B
 A: You simply need to remember the first relativity postulate to answer this one; essentially Galileo's postulate that there is no experiment that an inertial observer can do to detect their motion relative to other frames without making use of information from outside that frame. 
Therefore, the forces that any of the charges feels do not change from what they would be in any inertial frame: simply that calculated by Coulomb's law. If the charges are free to move, then they would begin to accelerate towards / away from one another (depending on their sign) according to Newton's 2nd law applied to them in a frame at rest relative to their beginning positions.
You can transform this force / initial acceleration picture to "your" inertial frame by Lorentz transforming the electrostatic field (encoded as the rank 2 Faraday tensor) and also transforming the force correctly: the apparent 3-force changes between the two frames and indeed one must use 4-velocities, 4-forces and 4-accelerations to calculate the dynamics of the system from a frame moving relative to the charges. The charges themselves and their invariant masses are of course the same in both frames. If calculated properly in this way, we arrive at the physically observed situation that both observers calculate the same trajectories for the charges.
A: If the charges are moving at (near) c relative to a given reference frame (there is no mention of a reference frame in the question, but there must be one, otherwise we wouldn't know there is any - inertial - movement whatsoever), but they are at rest to each other, then according to SR postulates we may as well assume that they are simply not moving at all. We are free to assume they are stationary, and that the chosen reference frame moves at (near) c relative to them.
In such case the forces remain unchanged, as long as we do not have any information concerning possible influence of this reference frame on the charges.
