[LS short box]

I haven't used EZ Wire. I have used Painless a few times.
You can use the hei wire to power the LS ECM since it will have 12 volts in start and run.
The LS ECM will need a constant 12 volt wire.
I've used Speartech and Howell LS harnesses and both provide one wire/plug to the alternator.
You need to run a large gauge wire 12 volts to the stud on the back of the alternator. I run that wire from the center stud on the starter, around the front of the engine along the oil pan. I used rubber lined cable clamps using the oil pan bolts to hold it in place.
In regards to the unused wires I trim them back but leave enough so you can see the labeling on the wire. Make sure the exposed ends don't ground out on anything.
I use Auto Meter gauges for my LS swaps. They have worked well.