Unable to fix misfire

Is this the reason that the engine was replaced? I included a diagram of the engine controls and the circuit that controls the #3 coil is a violet with brown wire. If this circuit were to get shorted to ground it would cause the coil to fail pretty quick. The easiest way to eliminate this circuit for testing purposes would be to cut the wire in half and run a wire from the power-train control module straight to the coil (overlay). If the misfire goes away then this will be your repair. The whine from the alternator could be faulty diodes which is very common on v6 mustang alternators, If they are bad enough, a cheap tester will pick that up. If the diodes are found to be bad, replace the alternator with the best one that you can afford because I have had tons of issues with certain (most) aftermarket alternators. Good luck and let us know how it's going!

If I can jump in here it sounds more like the coil is going out which is common. To be sure are two guides to help us with the testing and repair:

https://www.2carpros.com/articles/how-to-test-an-ignition-system

and

https://www.2carpros.com/articles/how-to-check-a-car-alternator

Please run down these guides and report back.

Not all short to grounds are created equal, there could be an intermittent short to ground. Coils just don’t go out for no reason, but if the trigger circuit of a coil gets an unintended ground other than the PCM millisecond ground from its transistors, the coil will burn up from staying on for too long and this could be from a wire rub through or pinched and barely making contact on and off to ground. I only said that because I’ve seen it many times.

The circuit in question is pretty short, being that the PCM is at the right front of the vehicle. Just do a real good visual at the PCM connectors where the support brackets for it are. This is a known area for wire chafes.

It absolutely could have gotten damaged during the engine swap! As long as there is no corrosion on the wires at the PCM, there should be no problem relating to battery acid. If you are uncomfortable doing any of the electrical work then I would recommend an automotive electrical specialist have a look. Expensive mistakes have been made quite often!