Unfortunately, there is much taken out of context and completely misunderstood.
First, “scholars consider at least half of the letters ascribed to Paul in the Bible to be non-authentic” is a bit misleading. Some scholars consider some books as non-Pauline (most notably the Pastorals)--but certainly the majority of scholars assert most of the letters ascribed to Paul were written by Paul. Perhaps you’re including Hebrews which does not name its author.
Even N. T. Wright suggests that 2 Timothy was likely written by Paul. There is quite a lot of debate re: 1 Timothy & Titus but the question is far from settled. While there some debate about Ephesians/Colossians, but most scholars lean toward authenticity.
1) Perhaps you are interpreting Paul through Martin Luther. Paul should be allowed to speak for himself. To take one phrase from Ephesians out of context misses the entire corpus of Paul. Chapters 4-6 of Ephesians focuses on behavior and living appropriately to the calling to be children of God.
I’ll point it out later, but even being saved by grace is not antithetical to Jewish teachings. Biblical Judaism never taught that people were saved by their good works. They were saved completely by God’s steadfast love. The sacrificial laws were not seen as somehow earning salvation or favor from God. Paul is echoing the words of the Prophets as did Jesus.
Within almost every letter written by Paul there is a call to ethical behavior including (but not limited to) forgiveness, caring for the poor, being gracious toward unbelievers, giving up greed, and avoiding anger, rage, malice.
The beginning of Jesus’ beatitudes points to the fact that no one can claim righteousness before God. “Blessed are the poor in spirit" (i.e., the spiritually bankrupt--those who cannot save themselves). Also, within the same Sermon on the Mount the discussion of God’s grace toward the good and evil (Matthew 6:43-48). Matthew 18 and Luke 15 (especially the story of the two lost sons, aka “The Prodigal”) are stories of the wide embracing grace of God.
2) Romans 10:4 “the end of the Law”--again, taken completely out of context. This also demonstrates a basic ignorance of Greek. Telos (“end”) means “purpose” or even “fulfillment” not necessarily destruction. In this case, the statement in Romans is completely consistent with Jesus saying he came to “fulfill” (pleroo) the law. (Note, pleroo and telos are often seen as synonyms).
Paul was a rabbi and a Pharisee (he never denounced his status as a Pharisee). Paul does not contradict Jesus. People have misread Paul or looked at him through the lens of Martin Luther who was answering questions the New Testament didn’t ask.
Even James uses the word teleo (verb form of telos) as to fulfill, "If you really fulfill (teleo) the royal law according to the Scripture, 'You shall love your neighbor as yourself,' you are doing well." (James 2:8)
To repeat, Ancient Judaism did not believe in “salvation by works.” It is all the grace of God, even for 2nd Temple Judaism.
3) “Women in their place.” The letters of Paul are occasional documents. In other words they were written to respond to specific situations. There are three groups told to be quiet in 1 Corinthians 14--those speaking in tongues without an interpreter, prophets when another prophet gets up to speak, and women who were interrupting the assembly with questions. The problem, as stated in chapter 14, is that the assembly had digressed into a cacophony of noise. Paul was addressing groups that were causing the disruptions and telling them to be quiet (14:26, 33, 40)*. Earlier in chapter 11 Paul assumes women will be publicly praying and prophesying in the assembly. In Romans Paul speaks of Junias who is a woman apostle and Phoebe, a deacon of Cenchrea. Phoebe is tasked with delivering the letter of Romans which includes, according to several scholars, the job of publicly reading the letter, and expounding on it. Again, you have taken this verse out of context.
*There is also linguistic evidence that vss 34 & 35 forms a quote from some in Corinth that Paul disputes in verse 36.
4) Since you quote John, how about using the entirety of John and its context? The gospel of John is filled with a high Christology. John equates Jesus with God (John 1:1, 14; John 12: 37-41 where Jesus is equated with YHWH--referencing Isaiah 6).
In John 20:26-29, Jesus accepts and does not correct worship from Thomas who exclaims My Lord and my God! Rather than disagree, Jesus affirms Thomas’ words by saying, “Because you have seen me, you have believed; blessed are those who have not seen and yet have believed.”
The book of Revelation, most likely by the same author (writing style is very similar and is traditionally attributed to John), is an example of Jewish apocalyptic writing. Jesus is certainly equated with God throughout that text--he receives worship, shares the throne with God, etc.
In Matthew 28:18-19, the apostles are told by Jesus to baptize in the NAME of the Father, of the Son, and of the Holy Spirit. Notice, “the Name” is singular yet followed with three names. Matthew is the most Jewish of the Gospels. Use of "The Name” would not go unnoticed. It is a euphemism for God’s name in Hebrew “YHWH".
5) False dichotomy. There is absolutely no contradiction between Paul and Jesus in the verse you quote. Paul never tells a follower of Jesus to take vengeance.
Jesus actually agrees with Paul that God will mete out justice--but it is not our place to take vengeance. Jesus says God will execute justice (Matthew 11:20-24; 12:36-37; 25:31-46; Luke 11:39-52; 12:16-21).
Throughout his letters, Paul calls on followers of Jesus to forgive each other and to extend forgiveness to those who persecute them (cf., Romans 12:14, 19ff, “Bless those who persecute you; bless and do not curse...Do not repay anyone evil for evil. Be careful to do what is right in the eyes of everyone. If it is possible, as far as it depends on you, live at peace with everyone. Do not take revenge, my dear friends, but leave room for God’s wrath, for it is written: ‘It is mine to avenge, I will repay,’ says the Lord. On the contrary, 'If your enemy is hungry, feed him; if he is thirsty, give him something to drink. In do this, you will heap burning coals on his head.’ Do not be overcome by evil, but overcome evil with good.”) There are other passages where Paul calls followers to forgive each other and to forgive and treat others (non-disciples) with graciousness.
6) Paul cares more for hierarchy (what, seventeen verses talking about deacons and shepherds out of thirteen books?) than the poor. I’d argue Paul spends little to no time on hierarchy of the church. He speaks twice as much about his collection in just one book than he does about “hierarchy” in Titus and 1 Timothy. In 2 Corinthians 8 & 9 he spends thirty-eight verses encouraging the Corinthians to respond to the physical needs of those in Judea who are suffering famine. He also makes reference to this collection in his other writings (1 Corinthians and Romans).
Just because Paul might speak more of theology doesn’t mean he is in any way inconsistent with Jesus’ emphasis on the poor. Remember, he is writing in response to situations in churches. Many of his letters are in response to questions asked by churches. This is a false dichotomy that proves nothing.
Basically, you’ve ignored the larger context of the gospels and the writings of Paul and you have cherry-picked statements of both Paul and Jesus taking them out of context.
