I hit Post too soon.
On your second part, the Catholic teaching is that anyone validly baptized is baptized Catholic, and therefore belongs to the Mystical Body of Christ, which is His Church. “Validly” here means in the name of the Father, the Son, and the Holy Ghost, with water. In other words, most Protestant baptisms are valid and your ministers baptize into the Catholic Church. “Invisible Church” is an expression we don’t like because baptism is not invisible.
Now, what happens to that newly baptized who attends a Protestant community of faith? He does not follow up with a Catholic Church life and falls off. The picture is better for an Orthodox who maintains a Church life in obedience to his bishop, receives valid sacraments of confession and the Eucharist and so the ordinary means fo salvation are available to him, despite the unfortunate schism of the past 1,000 years.
This is the Catholic ecclesiology in a nutshell; I realize that you are likely to disagree, but I want you di disagree with what we really teach rather than with what you think we teach.
Please consider applying your Catholic pinglist to this fine article.
The only reason I jumped in was to attempt to present something that was not irrational; clearly I failed. Please let me disengage gracefully.