Haruhi's Haven

1: The four children that were murdered were all stuffed inside the animatronic animals, but the fifth child tried to run, when the man in the Freddy suit chased after them. And when they were caught, they instead were shoved inside the jack in the box, not being killed instantly, but left to die for several days, only listening to the sound of a music box that they found comforting after a while. When they discovered the child's body, they kept it a secret and claimed they never found anything. The birth of the Puppet. The child that haunted the Puppet was the first to haunt the pizzeria, but not violently at first. Also, helping the other children cross over into the 'after life'. This would explain why you must chase after the puppet in the first death screen mini game, and why you must place the heads on the dead children in the second death minigame.

2: After the murders of the first five children, the Purple Man wasn't caught at that very moment, and continued to murder innocent children, but taking them in his car rather than stuffing them in Freddy Fazbear costumes. I believe this because in different death mini games, it shows Freddy bringing cake and happiness to the children, then the Purple Man proceeds to kill them.