I would say that the Catholic Church is the mother church.
They would have to. Since the Catholic Church is the global organization that the Apostle Paul farmed and spread toward Rome, the center of the Roman Empire.
Like's there no mention of the ten Apostles, even though there were at least ten of them; Twelve even.
Show where there's a distinction between the believers in Rome---or for any other city---and the church in Rome. You can't.
Also there's no mention of other churches we know existed anyway. Nowhere does Revelation purport to be chronicling all known churches.
True, unless you're willing to believe what the Church has believed from the earliest, that Peter's mention of writing from Babylon is a code for Rome, that, again, the whole Church believed from the earliest.
Not unless the Church says so. Yours is just an opinion with no weight behind it. The Church actually has an official teaching office, the college of bishops in communion with the pope and the pope himself (always a man and never a lady). What they say actually has weight behind it, because of the history of the organization and because the Scripture teaches that the Church should be overseen by bishops. These men (all men, never a lady among them) are them.
John was writing to test those who weren't Apostles to see if they taught as the Apostles taught. You should obey this scripture and test the spirits to see if they align with what the bishops teach in the Catechism of the Catholic Church.
The Church teaches all this. The Church further teaches that the true, accurate, historical expression of the One Christian faith is Holy Catholicism.
All I can say is that the Catholic Church is the Christian family, the official family of Christians. There are those like you who are only Catholic in heart but not bodily, and those like you the Church still embraces as fully Christian, as are those who are both in heart and bodily, Catholic. (The Church does not teach that those who are only Catholic bodily, but not in heart, are Christians.)
I am not Catholic in heart, mind, body or Spirit.
Where there is no Gospel there is no Spirit. The "Historical Gospel" of Jesus Christ is the heart and the center of the Christian faith. To believe the Gospel is to believe that we have been justified by faith alone. We are justified by faith alone because we are justified by Christ alone, Romans 3:26.
This is where we part company. It is by faith alone so that it can be by Christ alone. God does not accept the works or the obedience of sinners, even sinners that are indwelt with the Holy Spirit. Eating wafers and drinking grape juice is not going to make you like Christ, this is why salvation is totally and completely outside of ourselves.