Yes, God forgave the Ninevites. He relented from the disaster that He had said He would bring upon them (3:10), which was that the city would be destroyed in forty days (3:4) whereas God destroyed it 50 years later (https://www.gotquestions.org/Nineveh-destroyed.html)
The claim that the book makes is that the final verse is not a rhetorical question, but a statement. As I do not know Hebrew, I couldn't really follow the argument, but I think it basically says that the last verse can legitimately be either a question or a statement. Next, it addresses the previous rhetorical questions to see if the similar constructions imply that the final verse is a rhetorical question. Of course, whether the previous verses contain rhetorical questions have nothing to do with whether the last verse does. Only the context of the book can.
But the book claims that there are four supposedly rhetorical questions in chapter four (vs 2, 4, 9, and 11 respectively) and that none of them are really rhetorical.
The first question is by Jonah:
Ah, LORD, was not this what I said when I was still in my country? Therefore I fled previously to Tarshish; for I know that You are a gracious and merciful God, slow to anger and abundant in lovingkindness, One who relents from doing hard."
Now, the book claims that Jonah was wrong to think that God was too merciful to spare Nineveh, so this verse isn't as senseless as it might at first appear in their interpretation. The book says that the question appears to be rhetorical because it doesn't have a direct answer. However, the book goes on to say, there is no obvious answer to the question as required by a rhetorical question.
The book says this:
Jonah's question is rhetorical if its answer is obvious, but this is not the case. Since Jon 1 is silent on Jonah's motivations, the reader has no way to know what Jonah thought at the time. Hence readers of John 4,2 are likely to side with the sailors (John 1,10) and disown Jonah: disobedience to any God-given mission is surely wrong. If the answer to the question in 4,2 is not obvious, the rhetorical process breaks down.
It is true that Jonah chapter 1 doesn't say what Jonah said, but Jonah 4 does. That's what makes that question rhetorical, because the answer is implied in the question.
Isn't this what I said when I was still in my country?
"No, Jonah, you said that Nineveh has too many rotten fish. That's why you didn't go. Good question. Ask me another."
Jonah isn't asking God to remind him whether or not "this" is what he said. The answer to the rhetorical question is "Yes, that is what you said."
As for what "this" is, the answer is given in the context and in the verse. The context (2:10) says,
Then God saw their works, that they turned from their evil way; and God relented from the disaster that He had said He would bring upon them, and He did not do it
(I assume that the book has some explanation for this verse too, by the way. I haven't gotten to that part yet)
Thus, the context is that Jonah was angry at God for not destroying Nineveh. Verse one says, "But it displeased Jonah..." The "it" clearly refers to God's relenting from the disaster that He had said He would bring upon them. Verse three says, "...was not this what I said..." where "this" clearly refers to the same thing as "it" -- that God had spared the city.
Then the verse also explains what Jonah had said. Jonah says in verse 3 (paraphrased)
Didn't I say this before? That's why I ran away. For...
Thus, the reason he gives is what he asks if he had said, "I know that You are a gravious and merciful God, slow to anger and abundant in lovingkindness, One who relents from doing harm."
Therefore, the first question which the book claims is not rhetorical is indeed rhetorical.
The second question is by God: "Is it right for you to be angry?" It sounds rhetorical, but it isn't (according to the book) because it is answered. That is, Jonah at first doesn't answer God. However, God asks the question again in verse 9 (only referring to the plant now instead of God's mercy). Since Jonah answers, the question can't be rhetorical. Since the two questions are similar (and thus the same), neither question is rhetorical.
"Don't you want to see the movie?" asked John.
"Of course I do," answered Peter.
See, rhetorical questions can't have answers... or can they? Look again at verse 9
Then God said to Jonah, "Is it right for you to be angry about the plant?" And he said, "It is right for me to be angry, even to death!"
The answer to the rhetorical question that God asks is, "No, it is not right." But Jonah, in his anger says, "Yes", and says it rather strongly. God isn't asking Jonah the question to get an answer. It is a rhetorical question. Jonah says, "Yes," and God says, "Wrong answer."
"Don't you think you should say sorry?" asked John.
"No, I have a right to be mad!" insisted Peter.
"But you are the one in the wrong, Peter," replied John.
The final question in the chapter is the question in question (pun intended):
You have had pity on the plant... and should I not pity Nineveh...?
Their claim that it is not a rhetorical question is based upon the fact that none of the other so-called rhetorical questions are rhetorical. However, that is a false claim.
The interpretation of Jonah given in the book is:
Repentance is important but is not everything. God is merciful and just. "From this perspective, Jonah was absolutely wrong in imagining JHWH as a deity who cannot be expected to carry out a massive destruction of human (and animal) life".
However, Jonah should have known well of how God destroyed the first born of every child in Egypt, wiped out cities in the Israelite conquest of Canaan, and even destroyed many Israelites in the rebellion of Korah, when the fiery serpents came, and in the book of Judges when the Israelites continuously rebelled.
It's interesting how the book goes on to say
Nineveh was indeed destroyed, as were Sodom [and] Gomorrah.
It's funny how the author seems to forget that God himself said in Genesis 18:32
...I will not destroy [Sodom and Gomorrah] for the sake of ten [righteous people in it].
There is one big difference between Sodom and Gomorrah and Nineveh. No one was righteous in Sodom and Gomorrah, but everyone repented in Nineveh. One could argue that repentance doesn't mean righteousness. But notice how God says in Jonah 4:11, "[The Ninevites] cannot discern between their fight hand and their left," that is, they didn't know right from wrong. When they did learn right from wrong (by Jonah telling them that God would destroy them), they repented and turned from their unrighteousness.
The next argument in the book is that God's sparing Nineveh wouldn't have been just. But what law required that they be killed then? The law of sin and death, which applies to all humans, requires death for the sins of the Ninevites, and they did eventually die. What Justice is not served in the case of the Ninevites. If any of them did not face the second death, then the death of Jesus was the punishment for their sins, as it was for the Israelites (Hebrews 10:4). No Justice is contradicted here.
I didn't finish reading the book, so if you have any more questions about it, please let me know. Sorry for the super long answer :P