Chief Ragusa: I would hope that in that instance Richard would contribute English (and Angevin, Norman and Gascon) troops to defend Jerusalem, but the AI is just as likely to either refuse a request for military aid or to accept and then bungle the assistance so badly as to be of no help at all. It's a long distance for the computer to go, after all.
I'm not quite sure what you're asking re: the Patriarch. Also, I haven't figured out how to get the Pope to call crusades at all, if it's even possible in CK2 (and I really hope it is). Saladin does indeed still have a land connection between Syria and Egypt. The province in question is Eilat, just north of the Red Sea. I have plans to seize that territory as soon as I am able, which will not be for a while as we're under a truce now. Also, I don't want to provoke Saladin unnecessarily. I was extremely lucky not to get dogpiled back at Madaba.
Balian and Maria have a handful of kids. The eldest is
John of Ibelin, a real historical figure who became "the Old Lord of Beirut" after Jerusalem's fall to Saladin. IIRC, there is a "Sinai" duchy, but unfortunately it isn't possible to fabricate claims on duchies, just counties. So if I wanted to take it, I'd need to either fabricate claims for 2/3 of the counties in question or launch several holy wars to claim the requisite provinces. Once I have a large enough proportion (usually around 2/3), I could usurp the title and then dole it out to a vassal. Still, either way that's a long drawn-out process. There's unfortunately no principality tier in the game (they're all at duchy level), although in this AAR I refer to
historical principalities (such as Antioch) with the correct term.
The five tiers are barony, county, duchy, kingdom and empire.