There’s a problem with the wiring (harness) from the computer to the coils, or you have multiple bad coils.
Try swapping coil 4 with one of the others and see if the igniter fault moves to #4.
It’s possible some kind of electrical surge damaged the coils & alternator.
Circuitsmith is correct, you may have a problematic wiring harness.
One idea before starting down that path: Does this car seem to run ok now, and all the problems you reported above – relay clicking, etc – have been eliminated after the alternator change-out? If so, it is possible the computer is just reporting codes now it had already stored before.