Let us first understand the context of the teaching. Paul desires to be free of the thorn in the side. The parallel teachings of the desirability of being free of these thorns is found, as already mentioned by others, in the informing of the negative effect of not removing enemies from the Promised Land.
We must understand that one of the ways God teaches us is by arranging people and situations in such a way that the symbolism of the narrative in the past become teachings, instructions, guides for believers in the future. There used to be an art form called tableaux vivant, where the rich nobles of the court would arrange actors and sets in ways that conveyed a moral or a message. God prompted Sarah to have a desire to raise a family, and Sarah acted on it the way that infertile women of her time normally did, by finding a surrogate mother for Abraham's child. This led to a chain of events that resulted in the presence of Ishmael and Isaac. All this was to teach believers how to deal with law and grace, as Paul found out! Humans write with pen and ink, God uses people and events!
1 Corinthians 10:11Now these things happened to them as an example, and they were written for our instruction, upon whom the ends of the ages have come.
Romans 15:4For whatever was written in earlier times was written for our instruction, so that through perseverance and the encouragement of the Scriptures we might have hope.
The Promised Land is the picturisation of the new life that believers live, and all the old habits must be driven out in order for believers to be used as vessels of honour in God's household. Obviously the purer the life the higher the honour. Care for material possessions given up leads to being given the Kingdom of God for the little flocks.
Luke 12:32“Do not be afraid, little flock, for your Father has chosen gladly to give you the kingdom.
Care for earthly life being given up may result in being seated to the right and left of Jesus.
Matthew 20:20Then the mother of the sons of Zebedee came to Jesus with her sons, bowing down and making a request of Him. 21And He said to her, “What do you wish?” She said to Him, “Command that in Your kingdom these two sons of mine may sit one on Your right and one on Your left.” 22But Jesus answered, “You do not know what you are asking. Are you able to drink the cup that I am about to drink?” They said to Him, “We are able.” 23He said to them, “My cup you shall drink; but to sit on My right and on My left, this is not Mine to give, but it is for those for whom it has been prepared by My Father.”
However, Paul was attempting for an even higher prize, the exanastasis, the out resurrection, translated here as "the resurrection from the dead".
Phillipians 3:7But whatever things were gain to me, those things I have counted as loss for the sake of Christ. 8More than that, I count all things to be loss in view of the surpassing value of knowing Christ Jesus my Lord, for whom I have suffered the loss of all things, and count them but rubbish so that I may gain Christ, 9and may be found in Him, not having a righteousness of my own derived from the Law, but that which is through faith in Christ, the righteousness which comes from God on the basis of faith, 10that I may know Him and the power of His resurrection and the fellowship of His sufferings, being conformed to His death; 11in order that I may attain to the resurrection from the dead.
There are hints that Paul, unlike the sons of Zebedee, was not hoping this would result in glory for himself, but for being a blessing to his countrymen with whom he had a great burden for, but the details of that would involve a book or two, and not on topic, as far as the present answer is concerned.
What is important is that Paul is taking very seriously the command to let the words, the commandments of Christ, abide in him, in order to be found in Christ, so that through being in Christ, Paul would be the righteousness of God:
2 Corinthians 5:21He made Him who knew no sin to be sin on our behalf, so that we might become the righteousness of God in Him.
In order to be in Christ, Paul needed to be obedient, have the words of Christ found in him, eat His flesh and drink His blood. Obeying the instruction to confess, and be forgiven, and cleansed of all unrighteousness.
God recognised Paul as righteous, not by works but by grace, because of his belief in what Jesus said.
To answer the questions without complicating things by discussing all the other things that are packed into this very complicated passage:
The thorn in the side was a sinful way/habit (Grace always points to overlooking sin).
It was given to Paul to keep him from being proud.
God's grace was sufficient for Paul to be found in Christ.
All Scripture from the NASB.