I have 90 villagers, all the technology, and plenty of food. Unfortunately I still haven't solved any of the puzzles on the bottom row. after looking around in here, I see where there is supposed to be a new child born. But none of me villagers are dying anymore. They all are perfectly healthy even those that are 70. Do I just need to wait a while longer?

My oldest so far has been 79 ... Once you have full Medicine on the tech screen you have increased the age to which your villagers can live ... the age is even quite a bit older before the details screen shows them as elderly ...

You will have to wait for a villager to die jksmom. You've maxed your population. Once a few elderly villagers die and you have nursing mothers again, there is something particular you have to at that time for the "child" puzzle. You won't be able to do it until you have population room to breed!