Naw.
(1) The contents of your Post #28 does not show anything about any of the churches in the area being organized as "catholic."
(2) In Acts 9:31, the two words "καθ ολης"--a preposition and and an adjective--act upon and modify the substantive clause that defines the geopolitical region of Palestine, not the subject of the sentence "εκκλησια" (singular) or "εκκλησιαι" (plural) depending on whether you are reading from the synthesized critical text or the traditional Byzantine Majority textform.
(3) In translation the phrase "καθ ολης της ιουδαιας και γαλιλαιας και σαμαρειας", translated in 1611 A.D. as "throughout all of Judea and Galilee and Samaria", has the equivalent translated meaning of "comprisingκαθ=κατα (the) entiretyολης of Judea, Galilee, and Samaria."
(4) Aside from this clause, the core words "αι εκκλησιαι ειχον ειρηνην" mean "the churches had restpeace "; nothing else.
(5) Whether one here reads "church" (as force-fed into the Vulgate by Jerome, who chose to follow the Alexandrian school of theology and its texts); or "churches" (as in the KJV/AV by the panel of excellent translators who preferred the Byzantine Majority textform selected by the Catholic scholar Desiderius Erasmus as the best text available), there is nothing here to imply at all some miraculous juxtaposition of "kath holos" and "ekklesia(i)" in the same sentence to supply any connection whatsoever of this verse with the purely figmentatious human imaginative invention of a "Catholic Church" (proper adjective and noun capitalized).
Furthermore, regarding the meaning you want to read into Acts 9:32 as Peter somehow being ordained with sole apostolic dominion over the churches comprising the Palestian area, that is pure eisegesis, and not warranted by the grammar or its context.
In actuality, while it may have already been shown to Paul through his intimate experience with the independent autonomous assembly of disciples at Damascus, and while among the Jews there were Gentile Greek-speaking proselytes, it was not apparently known to Peter at that time that Gentiles could be spiritually reborn as followers of the Christ without first becoming converted to Judaism.
Apparently, that was a stumbling block for Peter, even when confronted by God by plunging him into the conversion and regeneration experience with Cornelius and his household, that led the Apostolic brethren to restrict Peter to evangelistic efforts with existing Jewish seekers, and the purview of gospellizing of Gentiles to the more cosmopolitan and better-theologically-trained Paul as the sole apostolic proprietor of that market segment.
You will recall that, following the dispersion of the apostles from Jerusalem, Peter being stranded at Antioch, showing a reversion toward Judaism, Paul coming and observing had to publicly figuratively spank Peter before the brethren for that character-spoiling unchristian partiality (Gal. 2:11-21).
All you can safely assume from verse 32 is that, while centered in Jerusalem, Peter legitimately occupied himself with the role of an itinerant evangelist, visiting Jewish churches in and about Palestine, having apostolic credentials. Verse 32 gives him no warrant as a proto-"Pope"; only as a roaming encourager and strengthener of the local ruling elders and their congregations (see 1 Peter 5, as well as 2 Peter 3:14-18 as referring doctrine-twisting troublemakers to Paul for correction).
You attempt to stretch this "catholicism" line a bit too far--in fact way too far--in your discussion points of Post #30, in my estimation.
It's helpful to got back to Apostolic times
There's the way the Church is defined in practice by the Apostles -- Peter and his Apostolic brothers preaching on the morning of Pentecost --- one flock, one shepherd --- guided by a Council of Apostles (i.e. at Jerusalem), message and vision to Peter confirmed by the Holy Spirit --- message being sent out to all the churches under the guidance of the Apostles, and thence to the successors of the Apostles made so by the laying on of hands --- already understood as "the Church as a Whole" (Ekklesia Kata-holos) by the time of Ignatius of Antioch ---
OR--- Of course there are other ways to parse it. One would be, based on your own personal bishopless interpretation (by definition schismatic) or EVERYBODY's separate personal interpretation (which would be chaotic).
One reason why the local churches cannot be completely autonomous, is that the teachings of the Church --- that is to say, not opinions of this or that cleric, this or that theologian, but the officiai doctrines -- are authoritative; if they were not, Christ would not have told us to resolve conflicts among the brothers by listening to the Church.
The tagline is a quote from Jesus: Matthew 18:17
If the Catholic Church is not the name of the Church founded by Jesus and inspired by the Holy Spirit for over 2000 years (despite numerous heresies and schisms) until the end of times when Jesus returns, What is the name of your church that meets the standards of the church founded by Jesus Christ?
The assertion "we are not a religion of the book" seems to me to be saying their domination over ALL of Christendom must be conceded and obeyed but when asked to prove this is God's will they find a need to at least try to substantiate the claim by appealing to the book (the Holy Bible). Quite circular reasoning for an organization that boasts it "gave" the world the Bible! Even Jesus Christ used the Scriptures to authenticate His authority.