Point: answering your own question is against the guidelines. (It is considered "spam" or proselytization.) Ask a question and let the people answer it.
I. Did the Catholic Church Give Us the Bible?
One (biased) interpretation of the historical facts results in the answer "Yes".
Other interpretations of the historical facts (equally biased OR unbiased) results in the answer "No" or "Not alone".
1a. The New Testament was written by the Church.
The New Testament was authored by individual Christians
- not by "the Church"
- and not by "the Roman Catholic Church"
1b) The Books of the New Testament were written by Apostles and other leading clergymen within the Church.
Not by "clergymen" in the sense that the word is normally used.
All of the authors were Christians, but none refer by name to the Roman Catholic Church.
1c) Recall 1 Corinthians 12:28, “And God has appointed in the church first apostles, second prophets, third teachers, then workers of miracles, then healers, helpers, administrators, speakers in various kinds of tongues.”
Here (as always in the New Testament), the word "church" has the meaning "congregation" and not "denomination"...and certainly not "the Roman Catholic Church".
2a. The New Testament was written to the Church.
Over-simple. See - for an obvious counter-example - The Epistle to the Hebrews.
2b) Just as the Old Testament was written to Israel, the New Testament is written to the Church. We see this most clearly in the Epistles, which tend to be addressed either to a particular church leader (Philemon 1:1, etc.), or a local church (1 Corinthians 1:2, etc.) or a particular group of Christians (1 Peter 1-2, etc.) or the entire Church (Jude 1:1).
Also: you assume that "the Church" is the Roman Catholic Church - but none of those documents attest so.
3a. Both the Old and New Testament were compiled by the Church.
Again: we have you assuming (in a retroactive way, called a "retcon" in comics) that some "the Church" existed at that time, and it was the Roman Catholic Church in particular.
One can equally well (in an equally biased and retroactive way) argue that "the Church" that did that was the Eastern Orthodox Church
or the Oriental Orthodox Church
or the Church of the East
The UNbiased characterization is that this was done by Christian officials of the 4th century at a few councils and synods
- some of those held in Greek-speaking territory (that is: traditionally, but not yet at that time, Eastern Orthodox)
- some of those held in Latin-speaking territory (that is: traditionally, but not yet at that time, Roman Catholic)
In any case, one cannot REASONABLY credit solely the Roman Catholic Church.
3b. Without the Church, you don’t have a clear way of knowing which Books belong in the Bible and which don’t.
The fact that practically all non-Catholic Christians disagree with the particular set of documents that Roman Catholics have chosen to include in their Bibles proves that practically all Christians DO have "a clear way of knowing" that and have chosen a clear way OTHER than the way chosen by Roman Catholics.
3c) As a matter of history, the Catholic Church gave us the Bible.
As a matter of ***a biased interpretation of history***
not as a matter of **the bare historical facts** (which do not refer to the Roman Catholic Church in particular).
4a. The establishment of the Church is mentioned in Scripture. Matthew 16:17-19
Yes, but what "the Church"?
Again: you mistake the word "church" to mean "denomination"
and assume that it refers specifically to the Roman Catholic Church.
Both are logical errors.
4b) Jesus set up a Church, . One of the ways that the Church fulfilled this commission was by creating the Bible, under the inspiration of the Holy Spirit.
Did you read that passage?
Did you read the commission given by Jesus?
Do you even know what the word "commission" means?
Clearly the Bible does not fulfill the commission given in that passage, and clearly it was not designed to do so.