Hey Jane, yea it is kind of confusing.  This is what i got from the passage you were writing about.

Jonah being angry -

I think it's kind of like how I feel when I read the story about the prodigal son, the son who left home after getting his part of the Father's estate that had been promised to him, I was like that's SO unfair!  I think that Jonah knew how bad the Ninevites were.  In fact everyone knew how bad the Ninevites were.  They had a reputation of being bad sinful people.  So God comes and tells Jonah to go and tell them to repent or God's going to wipe them out.  Jonah expects that these evil people will not repent and instead will stick to their evil ways.

However there is a change in events that Jonah was not ready for.  The Ninevites repented.  They showed how sorry they were to God by putting on sackcloth and sitting in ashes.  The king of the Ninevites implored all the citizens to plead with God to spare their lives.  They took Jonah's warning seriously and repented.  God seeing their repentance showed them compassion and forgave them and didn't destroy them.

Now to Jonah this was opposite of what Jonah thought the Ninevites deserved.  Jonah believed the Ninevites deserved to be destroyed. (Just like how I thought it was unfair that the prodigal son would be accepted back after squandering, wasting, all his money on stupid sinful self-indulging things).  Yet God forgave them.  Jonah knew God's nature.  He writes "   He (2) prayed to the LORD and said, "Please LORD, was not this what I said while I was still in my own country? Therefore in order to forestall this I (3) fled to Tarshish, for I knew that You are a (4) gracious and compassionate God, slow to anger and abundant in lovingkindness, and one who relents concerning calamity." Jonah 4:2. 

Jonah is angry because he doesn't think the Ninevites deserved to be saved from their fate that they had worked hard to achieve by sinning against God and being disobediant.  But what happens is that God teaches Jonah through the weed that grew to shade him.  (more later). 

I think Jonah's response to God's decision in regards to the Ninevites reflects our own saving through the mercy of God and the compassion of God.  We are the Ninevites and the prodigal son.  We've screwed up and totally gone the other way, but we didn't know.  God somehow shows up in our life and we are told the gospel.  We know and we accept and repent, like the Ninevites.  But when we see God being nice to other people we realize how they're being treated so wondefully to be excused of their sin and definite destruction through the compassion of God we're jealous and angry, we think it's unfair.  BUT, if we think about it again we have been so blessed by the grace and mercy and compassion of Christ.  What God did for the Ninevites, saving them from physical destruction is exactly what God does for us in eternal salvation.  God sees our sin, sends someone to tell us, hopes we will repent so He can save us.

The weed-

God was using the weed to tell Jonah how stupid Jonah was being by being angry.  "9   Then God said to Jonah, "Do you have good reason to be angry about the plant?" And he said, "I have good reason to be angry, even to death."
10   Then the LORD said, "You had compassion on the plant for which you did not work and which you did not cause to grow, which came up overnight and perished overnight.
11   "Should I not (12) have compassion on Nineveh, the great city in which there are more than 120,000 persons who do not (13) know the difference between their right and left hand, as well as many (14) animals?"" Jonah 4:9-11

Jonah's compassion on the weed was like God's compassion on the people of Ninevah.  He used the weed to help Jonah understand God's compassion and God's reason for saving the people of Ninevah.

I think that's mostly what I got out of it.  Jonah's story emphasizes the compassion of Christ that we are given through the gospel.  Ephesians 2:8-9 "8   For (3) by grace you have been saved (4) through faith; and that not of yourselves, it is (5) the gift of God;
9   (6) not as a result of works, so that (7) no one may boast."

God Bless!  Keep up the reading of His word!