If that’s the case, why didn’t Imam al-Hussayn (as) make dua (or something supernatural) to get water or avoid being killed for example?

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Because he wants the trial of Allah to play out naturally
In the end Allah wanted to try this Ummah, and to show how oppressed the Ahlulbayt (a) were, and also to elevate the status of Imam Hussain (a) and save Islam through him.