The Freelings were haunted by the ghost of Tweety.
- Nothing weird ever happened in that house until the canary died. Tweety came back for revenge.
- But Tweety's then targeting Carol Anne, the only one who wanted to give him/her a proper burial, instead of Diane, who wanted to unceremoniously flush him/her through the toilet, or Dana, who scoffed at Carol Anne giving him/her a proper burial. What a dick of a bird!
Tweety's death (indirectly) was what triggered the Poltergeist manifestations
- Tweety was not a ghost or haunting the family himself, but his death indirectly set off the hauntings because he got a proper burial on the Freelings' ground. The spirits up until that point had just been lost/lonely/sad, but seeing a deceased creature getting a loving burial on their ground while their own graves and human remains had been violated on that ground, was what made them flip and that's why hell broke loose then. That also neatly answers the often-asked question of "If the Freelings have been living on that ground for >6 years, why do the "ghosts" manifest just now?".
Kane's cult is related to the The Order from Silent Hill.
- Kane has no interest in "heading towards the light", rather he want's to build his own Otherworld paradise. Kane learning about Carol Anne's power was excellent for him for developing his paradise for reasons we don't learn about. For some reason, his reality is an icy version of our own, perhaps as symbolism for the lack of energy Kane has to work with. Like in the Silent Hill series, the monsters that Kane manifests as are symbolic of his particular psyche. Unfortunately, when Tangina offered her guidance to help Kane into the light, she unwittingly helped him complete his Otherworld, hence his laughter at the end of Poltergeist III. With his plan complete, sites associated with Kane will now take on the influence of his Otherworld as in Silent Hill, trapping some people within an abandoned nightmarish version of the area.