I second the Mahfouz recommendation, and add Yusuf Idris, and for a more modern name, Ala al-Aswani (I intend to read his book The Yacoubian Building in the original Arabic this year... or try, anyway, with the translation at hand).

Outside Egypt, there's Ghada al-Samman, who's Syrian, though her most famous work Nightmares of Beirut is about the Lebanese civil war, and Hanan al-Shaykh, who's Lebanese (both women). And I should mention Abdelrahman Munif, who is Saudi by birth at least, his "Cities of Salt" books are reportedly quite good. Unfortunately I haven't read entire works by any of these authors except Idris and Mahfouz (and saw the movie based on al-Aswani's book), so they're more suggestions than real recommendations. Heard good things about all of them, though.

Yes. Hence, you have to read one of each and one of "the other stuff".

There are some listed on the Wikipedia page Rebekah linked to, but there are many more possibilities.