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.