You have proved nothing whatsoever. You attempted to prove from the Catechism (the Magisterium) that the Magisterium is false.
The questions were not red herrings they were to give you the opportunity of proving that I was misapplying the word Church to the Magisterium. You didn't take that opportunity as you were smart enough to know that in doing so you would be blowing apart your personal theories regarding the nature and structure of the Catholic Church.
If you don't reply to the questions then I see no point in continuing this discussion.