Great Question.
I will only take one part of this (Paul)and leave the rest for others to comment on.
Why the Pauline letters?
For one, we have a great deal of reliability and certainty that Paul's letters are authentic. Most attempts to even discredit a few epistles as authored by someone other than Paul didn't even arrise till the 19th century. All the letters were considered authentic in one form or fashion by the early church and even appear in canon as early as 140 a.d.
There are no preserved lists of a Christian New Testament canon from the first century and early second century. Ignatius of Antioch, who wrote c. 110, appears to have quoted from Romans, 1 Corinthians, Ephesians, Colossians, and 1 Thessalonians, suggesting that these works, at least, existed by the time Ignatius wrote his works.[62] Ignatius does not appear to have quoted from 2 Thessalonians whereas Polycarp (died 167) not only quoted from 2 Thessalonians but also the Gospel of Matthew, Gospel of Mark, Gospel of Luke, Acts of the Apostles, 1 Corinthians, 2 Corinthians, Galatians, Ephesians, Philippians, 1 Thessalonians, 1 Timothy, 2 Timothy, Epistle to the Hebrews, 1 Peter, 1 John, 3 John.[63] Scholar Bruce Metzger stated "One finds in Clement's work citations of all the books of the New Testament with the exception of Philemon, James, 2 Peter, and 2 and 3 John."
The earliest extant canon containing Paul's letters is from the second century:
It is a canon compiled by Marcion, the founder of Marcionism (similar to gnosticism), a heretical sect. Marcion did not include any of the modern Gospels, only his Gospel of Marcion, which according to his enemies he had edited from the Gospel of Luke, whereas he claimed that it was their version which was edited from his original gospel. He includes ten epistles by Paul, omitting the Pastoral Epistles (Titus, 1 and 2 Timothy), as well as To the Hebrews.
There is also a list by an unknown author in Rome, usually named the Muratorian Canon. This includes all thirteen of the letters containing Paul's name; it includes other texts since declared to be non-canonical.
Papyrus 46, one of the oldest New Testament manuscripts (c. 200), contains the last eight chapters of Romans; all of Hebrews; virtually all of 1—2 Corinthians; all of Ephesians, Galatians, Philippians, Colossians; and two chapters of 1 Thessalonians. Because it is damaged there is no scholarly consensus on whether to consider the omission of a text definitive. Scholar Young Kyu Kim dated Papyrus 46 to the first century before the reign of Domitian (pre 81)[64] although other scholars have disputed his early dating. Source: Wikipedia
OK, so what? Why does this make them scriptural.
Paul was set apart for a very specific task to bring the gospel to the gentiles.
The Pauline letters are essential for non-Jewish folks to understand "why Jesus?"
If the book of Acts is trustworthy then we can trust that Jesus handpicked Paul to be His voice to the gentiles. The letters were widely circulated in the early church, and earned a scriptural reputation as the church rapidly spread through the known world.
I actually have some work I did a while back where I compared Paul's teachings verse by verse to those of Jesus. this is very significant because Paul and Jesus never met before His death. And, we have fairly certain evidence that the gospels were written down after Paul's letters.
Let me give you an example.
"And He will send forth His angels with A GREAT TRUMPET and THEY WILL GATHER TOGETHER His elect from the four winds, from one end of the sky to the other." Matt 24:31
"For the Lord Himself will descend from heaven with a shout, with the voice of an archangel, and with the trumpet of God; and the dead in Christ shall rise first. Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air, and thus shall we always be with the Lord. Therefore, comfort one another with these words." 1 thess. 4: 17-18
There are many examples such as this.