Just wondering if you still need to continue research after all the tech has been purchased? Also, when does the Golden Child arrive?

Once you have completed all tech levels, there is no further use for tech points. In fact, most of your villagers will not continue to research after all techs have been maxed. The Golden Child will not just appear. You have to do something specific to cause the arrival. You can check out the Virtual Villagers Guide if you need help figuring it out.