I have one person in second generation and never have any computer messages so she can never marry.
Can I at least adopt a child if she has no husband so that I can continue the generations?

The absence of emails in the game (marriage proposals, events, etc.) is usually the result of changing the system clock on your iOS device (either accidentally, or intentionally to make the game progress faster).

You can still adopt one or more children in the Special Upgrades section of the store, even if your little person is not married.

You can read more about the issues caused by clock adjustments in the first item in this post.