Although the oud can play microtonal intervals, does Middle-Eastern music still usually use scales that are made up of 7 diatonic notes (such as the Phrygian), that can be played on "non-microtonal" instruments such as the piano? In other words, are the scales that are used in the Middle East usually just a "mode" of Western scales?
No. Often, they are not modes of Western scales. On my algerian mandole, I really do need the 1/4 tone frets to play some of the mini scales that (when combined) produce a maqam.
It really gives a distinctive (uncomparable to western scales) colour to the sound. Although some of these mini scales perfectly fit the western Major or Minor tri/tetra chords... others (which are my prefered) just do not fit at all.
On my instrument there are only two 1/4 tone frets, and I think it the case for all algerian mandole. So it is nowhere as versatile as an Aoud you are refering to, but it is far sufficient to give access to a bunch of those micro tonal mini scales, which are NOT AVAILABLE for a standard western guitar fretted neck.
I don't remember the names of those musical forms. I have to search through my notes/links. I will update this answer accordingly with relevant names and information.