First of all welcome to the forum and congratulations on the build! That is a fun build, you will love them. Let me see if I can help a little.
1. The wiring diagram in the plans is correct and yes it is due to phasing.
2. I don’t use any internal damping, however others have and have had mixed feelings on how beneficial it is. I would say feel free to add it if you want. It is not going to hurt anything by adding it.
3. There have been some people who got bad power supplies. Typically they ended up returning them and getting a different one that didn’t have the ground loop issue. Unfortunately, it is impossible to say what will and will not have it without trying it. The way Amazon lists a product is under a generic name with multiple manufacturers making the “same” power supply. So when it goes out of stock, they restock it with a new supplier, who may or may not have properly grounded it. It is a pain, but I don’t know of any other solutions. You can try to pigtail it if you want, but you would loose out on power.
4. You didn’t ask, but I’ll throw this is there as well. If you feel you aren’t getting enough bass, you can bridger the RCA’s on the back of the plate amplifier. By doing this you will double your bass output.
I think that is a great idea of mounting the plate amps like you said.