I don’t normally do this, but since the game’s so open to interpretation, ideas just seemed to form naturally.

The murder and disappearance of the children is what caused things to go wrong. The evil of the act altered what were originally just highly sophisticated robots (since they can leave the stage at will). I.e. the restaurant was now haunted.
I don’t think the children themselves are haunting the animatronics, although the full-length scream sound effect lends some credibility to this theory. Since the extra sets of teeth are only mechanical, I don’t think the children or anyone else is actually inside any of the main four.
Initially it appears that the characters just have faulty programming, but later events such as moving objects and changing posters show that there’s more going on.

During the day, Freddy is a showman. As the leader of the group and the smartest, he’s the most concerned about making the show entertaining. That’s why when he learns about Mike, he gets angry at him for appearing without his suit on. He also seems to possess the most supernatural abilities.

Foxy was responsible for the “Bite of ‘87”, soon after the murders took place. Possibly some kid got him riled and he overreacted, and he was shut down afterward to prevent further incidents.
Originally cast as the antagonist, Foxy resents not being able to interact with the customers for so many years, and takes it out on anyone he encounters.

Chica is cast as the Big Eater- hence the bib- and is probably always hungry for pizza during shows. This translates to an animalistic appetite and personality, which is why she spends a lot of time in the kitchen. She’s likely to chew on anyone first before the others arrive.

Bonnie…? I got nothing.