Ok, I've got all my techs researched and I have the Golden Child but nothing's happening ... what do I do now?

The Golden Child will do something special when he is ready. There's nothing you can do to make him hurry (although it seems to happen faster if you can leave your game running on AC power, rather than turning it off).

Puzzle 12 is another story altogether, and it requires specific actions on your part to complete it. If you get totally stuck, you can refer to this post.