Can Egyptian nationalism become separate from Arab nationalism?

Sure, you can separate it. Just as likely you keep them together though. Mainly you say that you are the center of the Arab world or the best for running stuff. Plenty of Islamic states (I know they aren't all Arab) use propaganda that stretch back to pre-Islamic and pre-Arab histories. Saudi Arabia being one exception, as they demolished everything the rulers and their supporters thought connected too far into the past, plus a great deal of Islamic sites.
To be fair, pre-Islamic archaeology in Saudi Arabia is maing great strides in recent years. Though of course this does not apply to Mecca and Medina. The Saudi government does not seem to be using that for legitimacy, and I would be somewhat surprised if they did, but it's not like they are deliberately destroying traces of their past (they do when there's money to be made out of that, however, that mainly concerns Islamic sites).
 
Could rule by an Islamist Arab conqueror discredit Arab-Islam?
Very difficult after about 1000, AD as the majority of the population would be both Muslim and (vernacular) Arabic speaking, and most Christians (and basically all Jews) would be speaking some sort of vernacular Arabic as well, and largely using a form of Arabic (at some times, Jews would be using it in Hebrew script; Christian Arabic also had less Classical features) in writing too.
 
I think a successful Egyptian state under Muhammad Ali Pasha and his descendant can be a possibility, for example no Abbas Helmi I and in his place a more reform minded Khedive.

Getting rid of Abbas Helmi sounds fairly simple. He was in charge of the royal horse breeding program, so just have him take an unfortunate kick to the head while looking over the horses. That way you can have the throne pass directly to the western educated Sa'id Pasha. Sa'id's policies, if allowed to go into effect sooner and last longer, seem perfect for the formation of an independent Egyptian identity. Curbing the influence of the sheikhs and imams reduces regional factionalism, which in turn makes the nation feel more unified to its citizens. Sa'id was also a big railroad builder, which linked together areas that had previously taken days to travel between.
 
Could we end up with an Arab victory in 1948 lead to conflicts among the winners over how much of Palestine each would get to control? This would probably lead to the Egyptians against everyone else, which would separate Egypt from most of the Arab world...
 
Relatively limited. Some hundred loanwords, some influence on syntax, not much else AFAIK.
Although one could argue that the marginalization of Copts during the last millennia didn't help in preserving much of the substratum, especially in the Delta.
 
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