Hi and welcome! I'm glad there are still new RTW players coming here (and to the game itself). Now, on to your questions:

1. The AI is like that. It likes roaming about your lands when it's too scared to immediately attack but it's definitely thinking about it, and depending on the difficulty settings and if you move your armies away, that could go very up in its priority list. If you leave your towns lightly garrisoned and go away, it will be tempted to attack. If you're there though, and if the difficulty is not Hard or Very Hard, it's much less likely to.

2. No idea about cheating, though really - you should try playing without cheats (no one is yelling at you though ) It's funny when you get a slobbering idiot to rule your armies.
3. The candidates for marriage are spawned at random. You will get young guys eventually.
4. Each girl of eligible age has her own, independent chance to get a suitor. However if you have too many generals relative to provinces held, the game won't offer you any. There is hardcoded correlation between generals and provinces held. The more cities you have, the more adoptions/marriages you will be offered.
5. A general will want to marry a girl at random.
6. You can get a maximum of 4 children per couple, this is hardcoded. There will be a significantly reduced birthrate if you have an old wife or if you a have lots of generals but few provinces. Fertility is exactly as you put it.