Just have the various crusader snowball in success one after the other, have the Crusade of 1101 be a success and reinforce the first one and so on, if the Crusaders use their resources not to hold ground or retake ground lost inbetween the various expeditions you could have them have power projection over Egypt by the early 13th century by securing the Levant and Anatolia.
How would the demography of Egypt change if a crusader state had been set up in Egypt? Would Islam gain less converts than in OTL in such a scenario?
Would crusader Egypt get immigration from Egypt besides warlord as their companions?
Could a crusader state in Egypt avoid internal revolts overthrowing their rule?
How could this scenario impact the idea of chrisianity and what a christian is?
Islam would probably decline relatively quickly I'd say, at least in Upper Egypt and the areas affected by European settlement and trade, but it would stay relatively strong in the desertic areas of Sinai, Western Egypt and the Eastern Red Sea coast and on top of that the Delta.
Italians mostly, if the naval routes are secured you could have some others but all in all I don't see that much of a pull factor being present at this time.
Surely, who would be revolting anyway and why so early on?
There is so much stuff going on over Catholic Europe that it could really go in many different directions regardless of the survival of the crusader kingdoms.
A pretty minor factor, but one that could easily become relevant, are the various Coptic nations to the south. In the long run they could become the strongest supporters of the Copts within a Crusader Egypt.
Not so sure, the power projection from the South is pretty weak and the nations there were wary of angering the Mamelukes for example, so I don't think they would go much after the Crusader States, which probably have an interest in finding trade routes to the East altenrative to Persia or the Arab traders and the Nubian states with Ethiopia can potentially satisfy that.