Also, how is Libya doing?
The Muslim Brotherhood is thinking about reintroducing slavery in Egypt? Okay, what the actual fuck.
The Muslim Brotherhood ITTL is under the control of Qutbists, the dominant ideology of Al Qaeda and a popular ideology amongst those in Daesh as well. They are utterly amoral and utterly opposed to anything that doesn't subscribe to their incredibly narrow interpretation of Sunni Islam, as such I wouldn't put it past them to start debating whether or not slavery is consistent with their views.
The real problem is that they're so terrible at actual governance that it's hard to imagine them running a country as large as Egypt for any long period of time. Even if the way things are portrayed in the update seems to indicate that they're on their way out.
This is a pretty dark update. I do think it demonstrates that, IOTL, Islamism was the result of the failure of Nasserism, and so with Nasserism failing earlier, Islamism rises earlier.
The only saving grace here is that destroying a Pyramid would take considerably more explosive than blowing up a Statue of a Buddha. (I think that's one of the destructions in Afghanistan)
if they indeed blow up any ancient Egyptian sites aside from the Pyramids, I would imagine the international community howling at the destruction of heritage sites.
But it appears Islamism itself is beginning to teeter. As the update indicated, people are getting tired of the poverty and the oppression, and the thought of "retaking the Sinai" is becoming less and less useful as a rallying cry.
Can't the Shah survive and become the only sane man besides Israel and a source of stability in the Middle East?
Depends if he continued his same policies like OTL. And it also depends on how useful the US finds him as an ally now that the Soviets are finished as a world power.
If his reforms didn't work, and he remained an oppressive jerk, than most likely he won't survive.