"Al-Azhar is an important Islamic university."
Translation:اَلْأَزْهَر جامِعة إِسْلامِيّة مُهِمّة.
Is the order of the words "important" and "american" important in arabic?
Let me assume you mean Islamic instead of American. The farther an adjective is to the noun, and I mean that literally being written at the end of the sentence, the more likely will is be the main point of what you wanna say.
Think of it in English: Al-Azhar is an Islamic important university, or rather, Al-Azhar is an important university which is Islamic. (Emphasis that this important uni is Islamic) Al-Azhar is an important Islamic university. (Emphasis that this Islamic uni is important)