I'll take a shot at it:

1. Assuming you want the Coyote to control the cooling fan, which most do, agreed the cooling fan power wire and thermo wires in the RF harness are not used. The fan wire in the control pack can go directly to the cooling fan. The PWM controller would go in that wire. Side note -- your choice, but I haven't found another controller necessary. Had one in my 20th Anniversary Roadster, but haven't used one since. Builder's choice, right?

2. I'm a little lost in your description, but simply the Coyote system needs +12V on the Starter Motor Request (SMR) wire to signal the PCM to spin the starter. I connect this wire to the RF blue start wire off the ignition switch and remove the rest of the blue wires in the RF harness including the ones used for a clutch safety switch. However you make that happen with your pushbutton start is up to you. Just get +12V on the SMR wire when you want it to start.

3. What you describe is correct. I do essentially the same thing. There is an long alternator leg in the harness that is intended to go to the post on the alternator. I've used that in the past. For my Mk5 build, FWIW, I removed the alternator wire completely from the RF harness. The one in the starter solenoid group and the longer leg intended to go to the alternator. I'm going to run a single line from the master disconnect to the alternator. Many upsize that cable and that's what I'm going to do as well. I think the RF harness is 8 gauge. A little light maybe for the Coyote alternator. I'm going with 6 gauge, Same as I have on my Coupe. Some go to 4 gauge.

4. I think answered in #3 since they were related.

Hope that helps. I doing all these exact hookups on my Mk5 right now.