Funtime Freddy is severely mentally unwell even by animatronics standards but he's also a robot so wether it qualifies as an actual mental illness is debatable.
Technically yes. Over the five nights, you hear snippets of William Afton leaving his daughter alone with Circus Baby. Due to his ignorance, she is left alone and dies
Sort off. Elizabeth, the protagonist's sister, got killed by Circus Baby and then proceeded to posses her, and now tries to kill her brother to use his body to escape the Sister Location.
No, but the ending implies the character has been lied to and manipulated throughout, and a secret ending has the main antagonist attempting to emotionally manipulate the player.
The fact that Michael didn't die after being scooped by the Funtimes implies he uses or has used Remnant, a fictitious drug that keeps the soul bonded to the body even after death.
on night five of sister location, the night begins by turning on the lights to make sure the animatronics are there but you are shown the silhouette of dead technicians hanging on the stage.
It is implied that one of the animatronicd contains the spirit of an adult woman who was a mom. This is never explicitly said or shown in game, though.
A character explicitly says, "I kidnapped you", and she's correct. Also, the abduction of children is a major theme throughout the games, and all of them die.
No, but expect to see lots of debates in fandom spaces over what gender the robots are, as is typical for these games; Funtime Foxy is particular is referred to with both he and she pronouns.
A character is literally gutted alive,and later shown rotting (in 8-bit), but it's mostly implied; the screen flashes red, and that's it. However, as is typical of these games, horror elements are strong throughout.