1.You can't keep babies yet
2. If u haven't done all the events before going in to haven there will not be any new content after that at least not yet there's a lot of events to experience so you just need to look around for them if u think ur missing some stuff are just use the cheats.
Finally 3. So far as I know there hasn't been any events with Emily besides the walk and the beach events at the beginning maybe the new update has something new.
That's all I know hope it helps.