The passage in Jonah, like the Deuteronomy passage, speaks to the children not being responsible for the parent's sins. It does not speak to whether they are responsible for their own sins or not.
If anything, the verses you have supplied shows that children, because of their ignorance of what's right and wrong, are apt to choose the wrong. This is totally consistent with original sin - the inborn sinful nature of man.
That is just the point, original sin says we inherit Adam's sin and guilt, but God says no son shall die for the sins of his father, or the father for the sins of the son. God imposing sin and guilt on us for Adam's sin would be God violating his own law.
Deu 24:16 The fathers shall not be put to death for the children, neither shall the children be put to death for the fathers:
every man shall be put to death for his
own sin.
I disagree with your interpretation of Jonah. Look what it says;
Jonah 4:10 Then said the LORD, Thou hast had pity on the gourd, for the which thou hast not laboured, neither madest it grow; which came up in a night, and perished in a night:
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And should not I spare Nineveh, that great city, wherein are more than sixscore thousand persons that cannot discern between their right hand and their left hand; and also much cattle?
God says Jonah had pity on a gourd that he did not labor for or cause to grow, and then asks if he "should not" spare Nineveh that had 120,000 children. God implies that he created these children and made them grow. He implies it is the "right thing" to spare them. He also compares them to cattle which cannot know right from wrong.
As for your second comment, you are reading into it what you want it to say. It does show that a child must mature before they can understand sin and choose either to obey evil or obey good.
I do not deny that even little children sin, but I do not believe God holds them accountable until they understand their actions.