How many divisions should I keep around, roughly speaking? I'm playing as Yemen, having 2 divisions on Socrota and 2 on the main land, as well as a total of 4 ships. I could disband my transports probably, but I'm afraid that disbanding any of my land units will mean I won't be able to respond to revolutions.
Well, I've never played Yemen (though I once had a long game as Oman), but rebel size depends on the tax income of the province, IIRC. So if you have only poor provinces, they will spawn very few rebels, even if the trade value of the province is high. Since tax value portrays population etc. I imagine you could do with two infantry and one cavalry in one army. Maybe even just two infantry, since cavalry upkeep is higher. One cavalry might do too with a shock general, since Muslims get excellent cavalry. You can ship the army around with those transports, disband the ones you don't need. The rebels will take lots of attrition besieging your provinces anyway, since they are mostly desert. Do you plan to colonize eastern Africa or try to unite Arabia or what?
Stworca, did you play CK or CK: DV? It is much better with the expansion. Expansion adds more character mechanics and events, those are the best part of the game. Yes, the technology spread is fun, I wish other Paradox games worked like that too. Armies running all around Europe was definitely stupid, DV fixes that somewhat.
edit - Some +3 stability events require you to do something to upkeep the high stability, yes, since it is exceptional situation. It isn't always just money. However, there are lots of positive events that stem from high stability, like great persons appearing or bonus to tech research etc. Negative stability has some good aspects too; it increases colonists spawning. So for colonial nations it can be good to have the realm in constant state of internal strife under certain conditions, heh.
edit2- Heh, answering to your edit with my edit... You could try colonizing eastern Africa, barging into the Indian/Indonesian markets for spice trade (there are events favoring Muslims for that untill the Portuguese barge in), try to unite Arabia with fire and sword or something else and completely different. Reforming is painful in the short term, but pays off the long term.