2. When leaders in "The Vatican" violate Catholic faith and morals, they are not exemplifying what the Catholic Church teaches, but rather negating it.
3. What you said, verbatim, was "For sure. The true God is not the same god of the catholic church." This is a falsehood, since the True God is honored and worshiped by the faithful --- and dishonored by the unfaithful.
Lumping the faithful and the unfaithful together in one description, is unjust.
On the other hand, taking note of these distinctions may go a long way to clearing up your false witness problem.