All traits are inherited to children of the same gender. So if you're female, all your female children will have the same trait, they also get bonus abilities that don't show up (since they just copy their parent's history/trait). This also work for your spouse. If your spouse has a nice trait, the appropriate gender children also has it (one of the nicer things about the dynasty system). The only problem is some effects only work at the start of the game (warlord, naturalist, etc), so the children don't really benefit.
Ugly is broken though, as far as I can tell. This is probably because the <Dynasty_MaxNumChildren> definition in ElementalDefs overrides the trait, so you always end up with 4 children. It is essentially a free couple of customization points at the expense of being called ugly.
As for the age of marriage/have a child thing, children only comes available to be used when they turn 20. So that's the earliest they can marry and have children.
