Hi, one.
If not limited by the switching speed of the interrupting device, shunt impedance across the coil will do the limiting. That impedance consists of stray winding capacitance, external capacitance, and (for a non-air coil) losses due to eddy current flow in the core material.
I cannot imagine why ESR matters in normal cases. It would be ununsual for ESR to determine the interrupted current level and the external circuit will dominate once the interruption occurs.
Yes. See above.
Better that than non-resistance wire. But wire made from materials intentionally made resistive? Why bother?