Thanks Dory.
Yes, please carefully read all of the documentation, and my guide on this. It's best to map it out in LucidChart or a whiteboard first.
Inserting a child program into an Engagement requires special a campaign within the Program, but the Engagement handles the activation for you.
Yes, you will need some sort of kickstarter to Add to Engagement, but you do not need that for the child Programs in the way you described.