Muslims Conquest of Egypt

According to Wikipedia, the Muslim invasion of Egypt wasn't especially popular and Caliph Umar was opposed to it, but was eventually persuaded by Amr ibn al-As. WI the Muslims don't invade Egypt?

A couple of things:

1) What would happen to the religious situation in Egypt (Monophysitism)?

2) What happens when Gregory the Patrician secedes from the Empire?

3) What happens to Muslim conquests elsewhere?
 
Egypt

This seems unlikely in light of the rapid western expansion of Islam. But if the Arabs don't invade, it might have given the Byzantines more time to re-group and to consolidate their hold over the country. At some point, the Arabs will invade. Perhaps with a later invasion, they may have been defeated by a better prepared Byzantine army.
 
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