1) SR3 references for the Middle East include the aforementioned
Target:Wastelands, Dragons of the Sixth World, Year of the Comet, SOTA63, Survival of the Fittest and the upcoming
Shadows of Europe.
2) Persian Empire? Can't seem to find that reference?

There are mentions of Iran as an independent state in
DotSW and
Black Madonna. Regardless if there is any such thing then it would be based around Baghdad the traditional Persian capital.
3) I think you may have misread something. The fact that the King of Saudi Arabia was
chosen to be the new Caliph doesn't mean he was chosen democratically. In fact, Ibn Eisn is mentioned as being a cleric in several texts which in Islamic terms means an ulema or iman. Relevance? Well, the original Caliphs were chosen and aided in governance by a council of ulemas (clerics and religious scholars who interpret the
Sunna and developed the
Hadith in Sunni nations). This is still essentially how things are in Saudi Arabia today and looks like the way it will be in the Caliphate. The kingdoms and principalities that make up the Arabian Peninsula do not have a tradition of democracy for the most part and are very happy that way. Even though they're best described as enlightened monarchies, the absolute sovereign has a number of obligations to his people - this translates to things like no one pays for basic utilities (electricity, water, gas, sanitation), basic transports are free, lots of social works paid for by the State, etc - and their rules have gone largely uncontested (except by other royals) for the past 100 years or so.
4) Tehran is described in
Survival of the Fittest. It is essentially a ruined ghost town (literally) and a haven for persecuted metahumans and critters. Aden doesn't allow it to be rebuilt.
It was destroyed in 2020 when Ayattolah Hammidulah declared metahumans unholy and diabolic and called for a
jihad against them. The great dragon and sirrush Aden swooped in and leveled the city in retaliation. It is no longer the capital of Iran although several canon references point to the fact that the nation continues to exist (incl.
T:W).
Regarding Ibn Eisn, the Islamic Unity Movement and the New Islamic Jihad (all introduced in
Year of the Comet), the important thing to note is that Ibn Eisn is preaching jihad and hasn't declared a jihad against anyone (yet). Part of the reason behind this is probably that the memories of the Second Ottoman Jihad (EuroWar2) is still pretty vivid. Furthermore, the NIJ acts as a radical faction within the IUM and doesn't represent the movement as a whole (sort of like the Fatah faction of the Arafat's Palestinian party). To complicate matters Lofwyr was involved in the IUM's inception and doesn't like the way it's gone and Aden has his claws in the pie as well.