Why are Paul’s writings so prominent in the Bible?

1) Why are Paul’s writings so prominent in the Bible?

I'm not sure what you mean by "so prominent". They don't seem unusually "prominent" compared to the rest of the Biblical authors' writings, relative to their context, anyway.


2) Paul was not a disciple of Jesus.

Er...yes, he was.
Not while Jesus was on Earth, but still...there is no disputing that Paul was a disciple of Jesus.


3) His writings seem a lot harsher than what Jesus said, too.

Odd. Perhaps you should read more carefully - both the Gospels and Paul's epistles.


4) So why are Paul’s writings treated as so important?

They are in the Bible.


5) I just wonder why I should give weight to what Paul writes compared to what Jesus said, for example.

The Bible teaches us that two of Jesus' hand-picked apostles evaluated and approved of Paul's teachings.
The Bible also teaches us that later Paul himself became an apostle.
So: in order of "authority" we have
- the teachings of Jesus / God
- the teachings of the eleven "good" apostles that Jesus himself picked
- the teachings of the other apostles mentioned in the Bible (including Paul)
- the teachings of the other Christians found in the Bible

But note that this is a sort of pointless list, as there seems to be no contradiction between these teachings.

We accept Paul because his teachings have the authority of the eleven original, good apostles, whose authority comes from Christ.

Paul was a disciple of Jesus and an apostle.  His writings are of strategic importance because, unlike the other 12 original apostles, Paul was an expert in the Old Testament Law, a "pharisee's" pharisee.  He had greater insight into what freedom Jesus offered his people more than any other.
  Paul's theology sees eye to eye with what Jesus said and taught.  Why you think they were "harsh" is beyond me, but then that's common thought in Christendom.

Perhaps because of what he wrote in Gal. 1:12 and 1 Cor. 14:37.  Have you read those "writings" yet?

Paul was made an apostle to the nations. Why do you think Paul was harsh? All of his teachings are of God who inspired him to write the Books he did. He taught Christian teachings. Was seen as a beloved brother by the other apostles of Jesus Christ. God used Paul in a large way to start congregations in many lands. All Scripture is inspired of God and important.

The LORD personally appointed Paul as apostle to the believing Jews and Gentiles to bring them together as one in the early church.


READ THE SCRIPTURES



Acts 9:15 KJV — But the Lord said unto him, Go thy way: for Paul is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:


Romans 1:1 KJV — Paul, a servant of Jesus Christ, called to be an apostle, separated unto the gospel of God


1 Corinthians 1:1 KJV — Paul, called to be an apostle of Jesus Christ through the will of God.


1 Corinthians 9:1 KJV — Am I not an apostle? am I not free? have I not seen Jesus Christ our Lord? are not ye my work in the Lord?



2 Corinthians 1:1 KJV — Paul, an apostle of Jesus Christ by the will of God


Galatians 1:1 KJV — Paul, an apostle, (not of men, neither by man, but by Jesus Christ, and God the Father, who raised him from the dead;)



Ephesians 1:1 KJV — Paul, an apostle of Jesus Christ by the will of God, to the saints which are at Ephesus, and to the faithful in Christ Jesus:


1 Timothy 1:1 KJV — Paul, an apostle of Jesus Christ by the commandment of God our Saviour, and Lord Jesus Christ, which is our hope


1 Timothy 2:7 KJV — Whereunto I am ordained a preacher, and an apostle, (I speak the truth in Christ, and lie not;) a teacher of the Gentiles in faith and verity.



Titus 1:1 KJV — Paul, a servant of God, and an apostle of Jesus Christ, according to the faith of God's elect, and the acknowledging of the truth which is after godliness

Because Jesus agreed with everything that he wrote.

Jesus Christ declared that God’s Word is truth. John 17:17

Same reason any of the other texts are included. Because the Holy Spirit guided the bishops of the Catholic Church to include them, when they compiled the Bible in the 4'th Century.

JESUS DIDN'T FOUND A NEW RELIGION:
The Roman Government used Theophilus, Luke, and Paul, to establish the COUNTERFEIT church of Paulism/Romanism which later became Catholicism and other denominations.  The REAL APOSTLES' involvement is mostly fabricated by Luke. 

EPISTLES WRITTEN BEFORE GOSPELS:  
The APOSTLES were still alive and preaching in 67 AD. They didn't write at first because they followed Jesus' example: No one can steal and mistranslate from another's mind. Paul didn't know he wasn't supposed to be writing so all his letters were written before the first Gospel.

Luke who worked for Theophilus, Head of Religious Affairs for the ROMAN GOVERNMENT, infiltrated the 'church' by becoming paul's disciple.  Neither Luke nor Paul was ever disciples or Apostles of Jesus.  After Mark and Matt. were written, Luke borrowed them to write Luke and Acts, and never returned the original manuscripts to their rightful owners. 

Of the 66 books that make up the Bible, Paul's contribution was only 13 short letters/epistles (short compared with many far larger books in the Bible). The percentage of his contribution is very small. Moses wrote far, far more than Paul ever did! But Paul was a scholar and a linguist, deeply rooted in the writings of Moses, the prophets and the Psalms. So, when he was miraculously converted from being a Pharisee to being a Christian (a disciple of Jesus, in other words) he was uniquely placed (by Christ) to speak out publicly and to write persuasively of the things of Christ.

You are quite wrong to say "his writings seem a lot harsher than what Jesus said". Have you never read what Jesus said in Matthew chapters 23 and 24? Forgive me if I am wrong, but you sound as if you are just repeating what other people have told you, and you have never studied the writings of Paul at all. Perhaps others have just cherry-picked bits out of context and spoon-fed you those. Find out for yourself.

Read the bible and find out. Your question shows that you haven't read enough of God's word to be able to understand not only Paul's life as an Apostle but understanding God Himself and His nature.

Paul’s letters strengthen the Christian organization. Read this article: https://www.jw.org/finder?wtlocale=E&docid=1102009474&srcid=share