Who Caused the Bite of '87?
The Bite of '87 was an incident that took place in the pizzeria a few years prior to the main plot. In this incident, an animatronic violently bit a customer's frontal lobe off, thus leaving the victim in a vegetable-like state. The Phone Guy briefly mentions this incident to you during the first night, but he never revealed which animatronic did the biting. This incident caused the restaurant to decrease in popularity, and it led to the animatronics to only roam at night.
It is commonly believed that Foxy was responsible for the incident. One reason as to why this is generally believed is because Foxy is the only animatronic that possesses sharp teeth. There's also the fact that his attraction was closed and that he's noticeably in more disrepair than his fellow animatronics. He's also shown to constantly hang his mouth open almost as if it were broken in an undisclosed accident.
Freddy himself is also a prime suspect. In the East Hall, there is a poster that explicitly states that a one mustn't touch Freddy. There are also hand-like markings on Freddy's face which most likely implies that someone tried to push him away.
Another suspect for the bite could be mangle, as he/she hangs down from the ceiling and seemingly "Bites" your forehead. Just like Foxy, it is also in disrepair, having a hanging jaw which is big enough to fit at least a human's forehead.
Also that paycheck there says 1987. The first time we saw a date in the fnaf series and since MatPat from Game Theory thinks that fnaf 1 takes place in 1993 makes it so it can't be foxy and freddy who did the bite of 87.
How Are the Animatronics Moving Around? A few years prior to the main events of the game, five children were reported to have disappeared in the restaurant. According to the authorities, the children were lured into the backroom by a man disguised as one of the mascots (most likely Golden Freddy), and were then presumably murdered. The man was later arrested, but the bodies of the children were never found.
Later on, a few parents posted complaints to the health board that stated that the animatronics were emitting foul smells and that blood and mucus was leaking from the animatronics' eyes and mouths. It is thus implied that the children were stuffed into the suits after they were murdered by the imposter. It is also implied that the animatronics try to hunt down the security guard, because they believe that he was the person who murdered them. A few things supporting the idea that the animatronics are possessed by the slain children include the screams and laughter. For example, if one were to listen to the full scream that the animatronics emit, one would notice that the screams sound eerily like a child's scream. Freddy's demonic laugh is also actually a little girl's laugh slowed down 100 times.
Who is the Killer?
If it is indeed true that a murderer lured the five children into the backroom to murder them, then one must ask the question: who is the murderer? There isn't anything official about the Killer as of right now, but what is commonly accepted by the FNAF fandom is that the children's murderer was most likely a former security guard. The reason for this assumption is that the killer seemingly had access to the backroom and to a Freddy Fazbear costume. The police did arrest a man, but the identity of the killer was never revealed.
In a recent interview with Scott Cawthon, the video game's creator, he had stated that either the Phone Guy or Mike Schmidt were involved in the Missing Children Incident or the events that led to the closing of the restaurant. Either character's back story might be revealed in the video game's sequel.
What is even more absurd than what is stated above, is that the animatronics themselves murdered the children, and that the managers of the pizzeria shifted the blame on a completely innocent person.
Apparently in the prequel for the first game, it is revealed that a Puppet lured the children away and murdered them. This is shown in the mini-games that appear whenever your player character gets killed by an animatronic. This is still being speculated, however.
The most solid theory is the one that William Afton, from the novel, who gets in an animatronic mask and lures kids to a secret back room and kills them, but leaves the bodies. The minigame seen was the puppet giving the children life. The puppet is a good guy.
Helpy is Michael Afton, in a way
This theory is a very simple one. Helpy is often seen as the player character in the minigames of FFPS. He is never seen active in the 'real' part of the day (the office part where you have to fend off animatronics while you're printing/buying/cleaning things), and is likely just a bobblehead. This theory suggests that Helpy is a Freddy design customized for Michael, and that Funtime Freddy is based off this design rather than the other way around.