Learn Turkish: Kızın durup dururken baklava yiyeceği tuttu. - The girl had a sudden urge to eat baklava out of nowhere.

This is because of how the sudden urge structure works grammatically. The urge to do something "belongs" to the person. The literal translation of this sentence is closer to "The girl's going-to-eat-baklava took hold." Therefore, kız takes the genitive suffix -ın, linking it to the 3rd-person possessive ending on yiyeceği.

How exactly does yiyeceği tuttu mean "had a sudden urge"?

The formula [Verb] + -(y)AcAk + [possessive] + tutmak is an idiomatic structure used to express that someone suddenly and unexpectedly wanted or decided to do something. Tuttu literally means "caught" or "took hold," so the phrase paints a picture of an action (eating baklava) suddenly taking hold of the person.

If the urge happened in the past (tuttu), why does yiyeceği use the future participle -(y)AcAk?

In this idiom, the future participle -(y)AcAk (which softens to -AcAğ- here) acts as a noun describing the intended action. At the exact moment the urge "caught" (tuttu) her, the act of eating the baklava was still in the future. The tense of the sentence is always determined by the final verb, tutmak.

What is the literal meaning of durup dururken?

It literally translates to "while standing and standing," combining the verb durmak (to stand/stop) with the connecting suffix -(y)up and the "while" suffix -ken. It is a very common fixed expression in Turkish meaning "out of nowhere," "out of the blue," or "for no reason."