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!

No, it was replaced because it was about to throw a rod. I did not have misfire issues until after the engine was replaced. If there was a short to ground then why did it work fine for two weeks after replacing the main computer?

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.

Yes, the coil is going bad. And we replace the coil, and it goes bad again. We have replaced these coils three or four times and they keep going bad. That’s why we replaced the main computer. It is indeed still cylinder 3 and we cannot find the reason why it keeps burning through coils. I really need help.

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.

Could a wire have been damaged or pinched during installation of the new engine? Perhaps that is causing the issue? And how would one go about finding that wire and potentially fixing the problem? If you’ve answered this already I apologize. I’m no mechanic and I’m trying to solve be problem as quickly and cheaply as possible.

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.

But is it possible that something happened during the installation of the new engine? I just know I never had this issue before the swap.

And I should be paying attention in particular to the wire/connection for cylinder 3 yes?

And finally, should I take it to an “auto electrician”? I do know at some point there was some corrosion around the battery terminal don’t know if that could also potentially happen to where wires connect to the PCM. Sorry for all the questions, my head is just spinning and I’m desperate to find the root of the problem and fix it.

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!