I'd say Diplomacy and Stewardship are the two most important stats. Diplomacy to keep your Lords happy (especially in the beginning of your reign) and stewardship for your demesne (As they will heavily complain if you go over the limit and having a strong demesne will help greatly putting down rebellious lords). Note that good traits really help in the Diplomacy part as well. Also, the relationship with the Pope is crucial, as you'll end up excommunicated with a rebellious Lord if the Pope doesn't like you (They do that like every single time). Basically, for me, all is stable until a new heir comes. Then everyone rebels (like now in my game) and I have to try to put them down one by one. Then, after a few more small incidents, everything is stable till my next heir comes along.
You can only help others in their War if you have an Alliance with them and they ask for your help or if they are fighting heathens. I've had it happen several times.
