You do not show that two things are identical by showing that one gives rise to the other. You're again ignoring the difference between nomological supervenience and logical identity.
I did not cite your facts as evidence of mind-body dualism. The point is that (contrary to your earlier suggestion) they in no way favor reductive materialism over its rivals.
I'm a reasonably intelligent human being who's seen this debate more than a few times, and I'm not familiar with this terminology -- or sure why you're assuming your audience here is.
A nomological truth is a law that does not express a logical necessity. The laws of electromagnetism and gravity are good examples: though true, there is no logical reason that they
had to be true.
As for supervenience: A-properties
supervene on B-properties if there cannot be a difference in A-properties without there being a difference in B-properties. (In this case, the A-properties are mental phenomena, while the B-properties are the physical processes that give rise to them.)