Try using the Ctrl-S to quick save the game. Ctrl-L will do a quick reload. If you are crashing chances are you need to upgrade some driver somewhere. I have been playing MTW since it came out and since loading version 1.1 I have never had it crash.

Often kings will have children even when they are quite old. In my current game the king had 3 children in the last 3 years of his life. If it really looks like you might not have an heir by the time your king gets to 65 or so you can always take preemtive steps and use the cheat code that will cause a male heir to be born the next year. The only time this doesn't work is if your king has 6 brothers all waiting to be king then you can not have another heir as 6 is the max. The cheat code is keyed in while on the strategic map and is .unfreeze. and make sure to include the periods on either end.

Heir stats are worked out when the heir is born but it isn't until he is of age that he is capable of becoming the ruler and then gets placed at the top of the list (obviously).

Your king's influence affects your ability to make treaties and also I think has some effect on the size or cost of crusades and most importantly, controls happiness levels at home. However, once you gain a certain size the AI no longer sees you as a viable strategic partner because you probably got big by warring on your neighbors. Why would they want to ally with a wormonger? You will be hated, envied and attacked at every sign of weakness. Enjoy it, it is Total War after all.

Enjoy, MTW is one of the best games ever created!