About the map, I must say again that it is an approximate one, so the Ayyubid Sultanate may extand further into Anatolia. In the 1170's, Byzantines expanded mostly by annexing the Sultanate of Rum and the Ayyubids got most, but possibly not all, of Danishmendid emirate, including those which the Seldjuks of Rum had attempted to conquer.
Also, Jerusalem border may extend further west and south into Arabian desert and Hejaz. Without going deep, they could make the Sharifate of Mecca a client state, supporting/funding one's bid for power (like Qatada ibn Idris) and garrison some ports, including Aden.
Edessa has been victim of bad luck in its involvment in the Danishmendid wars, Ayyubids taking Edessa itself in the 1170s and the remainder being absorbed by Aleppo.
The fall of Edessa has been also the occasion of a reassertion of royal authority of Jerusalem in northern Syria as the Royal Army has an occasion to intervene.
Aside of Tyre, the price paid for Damascus in 1129, there is several Muslim lords vassals of Jerusalem or Tripoli, notably in the Bekaa valley (maybe Baalbek and Chayzar) and also Palmyre, but that an oasis disputed that is, according to the time, vassal of either Jerusalem or Ayyubids or even both.
On the economic and social ground, the relative period of peace and the great prosperity enjoyed by Jerusalem after its subjuguation of Egypt would lead eventually to the rise of a native merchant class which would compete with Venetians and Genoeses, whereas IOTL the much reduced Jerusalem (after the third crusade) was reliant on them. Expeditions in the Red Sea, into Yemen and Hejaz to secure trade routes to India would be part of that development. A significative rift could be observed at the occasion of the conflict between Venetians and Byzantines, the latter being more or less allies of Jerusalem, and its consequences in Egypt.
Culturally, the big trend would be a progressive rift between Latin states and the Church, with maybe an early form of gallicanism.
Indeed, as it was often observed, while newcomers were used to be intransigent in politics like in religion, local Latin rulers have become pragmatic, used to some form of real politik, and especially religious tolerance. The conflict might take long to show but it will surely be meaningful, and lead to an earlier questionning of the relations between Church and the Royalty than in West due to the more diverse religious environnement. Already, it could have been observed that Jerusalem, Tripoli and Byzantines sought to avoid a new crusade after the fall of Edessa, one that Church was willing to make, temperating the gravity of the situation (insisting in the internal side of the affair), and it was a relative success (still some people willing to engage but no organized crusade by barons).
Jerusalem could become an hospitable land for exile of ''heretics'' (we could see Cathars).
In Egypt, the Copts would enjoy a more privileged position in the Fatimid administration and army, but they wouldn't necessarily like the intrusion of Latin and Greek priests and some could eventually join the ranks of a nationalist movement along Muslims. In the long run, even if they succeed, while Jerusalem holds onto the isthmus of Suez, and maybe Damiette and Alexandria, Egyptians would not represent much of danger, especially after the Mongols leave. The Mongol interlude could even be the occasion of some plots to overthrow Jerusalem domination.