What you hear down range is a little more complicated. The first thing you'll hear is the bullet whizzing or zinging past. If it's still traveling faster than the speed of sound, I think you'll get a sonic boom off it rather than a "zing." Then you'll hear sonic booms from further back along its path, all the way back to the weapon firing as soon as each noise reached you ...
From experience it sounds like a crack and echoes, no whizzing or zinging that I remember, and it gives the unnerving feeling that you don't know where it came from. The zinging you get when the bullets hit something and ricochet or tumble in different directions.
Your hypothetical hypervelocity magnetic gun wouldn't have the chemical boom. No moving parts, so no mechanical sounds. Maybe a cool electric whir if you want.
A rail gun gives off an enourmous noise when fired, but a coil gun probably would not. On the other hand, both would have to be extremely rigid not to give off som mechanical noise when fired. Transformers in power supplies are commonly dipped in glue or varnish to prevent them from vibrating due to the magnetically induced forces. I think it's called magnetostriction.
There are various tricks that are used to reduce the effects of recoil on the shooter. The most effective is to direct the gasses leaving the barrel in a convenient direction. Pads, springs, and etc. add weight and steal bullet energy but reduce bruising.
Not sure what you mean here. Viscoelastic or rubber pads are used to spread the recoil force in time, i.e. reduce impulse. The mechanism of automatic or semi-automatic guns use some of the gas pressure to move the bolt and reload the gun.
The game issue I'm curious about is how the bolter difers from a sniper rifle. I think for the same energy heavier bullets penetrate better than light ones (the v^2 thing), so maybe the bolter could be better against light armor and the sniper rifle better against the heavies?
Depends on the armor, the bullet and the velocity. A small fast bullet delivers more energy to the target than a large slow one. To penetrate a hard shell armor you would probably want a fast high density projectile with a small cross-section. The same would probably apply to the fabric of kevlar or similar body armor. Maximum energy transfer per area to punch through the shell. To penetrate something softer, for example shooting at someone that is under water a slow heavy bullet should work better. At high velocities all objects appear as a hard surface, assault rifle bullets can shatter when they hit water for example.
As a comment, it is easier to hit a target at long range with a faster bullet. This is both due to that the trajectory is flatter and that you don't need to lead a moving target as much. However, light bullets are more easily affected by wind, rain etc.
