Question: What exactly is the red slime on the body of Carol Anne and her mother after they are rescued from the another dimension?
Question: What exactly did the ghosts want with Carol Anne?
Answer: They were partly attracted to Carol Anne because she she was born in her house.
Question: Why was only the Freelings' house sucked into the vortex? Since it was discovered that the developer only moved the headstones but left the bodies, shouldn't other houses that were also built over the cemetery have also been dragged in?
Answer: It seems that the majority of the activity was focusing in on the Freeling house exclusively. It's not fully explained why they were the only house affected, but there are a number of possibilities. Possibly because it's where the highest concentration of spirits were at unrest. Possibly because it could be inferred that the Freelings moved in first given Steven was involved with the company that built the community, and thus they became the first targets. And possibly because they were trying to get to Carol-Anne since she was an easy target.
Also, it is mentioned in the movie that Carol Anne was actually born in the house. That likely caused everything to focus on her.
Answer: A poltergeist haunts a person rather than a place. Though building the neighborhood over their graves is what initially disturbed the ghosts, they are fixated on Carol Anne.
Question: Is there any particular reason the ghosts are still there after Tangina has declared the place clean, other than these are just the biggest, baddest ghosts on the block? I'm fine with that explanation but I always wondered if there was more to it.
Answer: Tangina may have believed the house was "clean," but the dark spirit she called the "Beast" was more powerful than she realised and was preventing the other spirits from moving on. The real estate development that the Freelings' house was built on was supposed to be a former cemetery. However, no-one, including Tangina, knew that the bodies were still buried there (the developers had only moved the tombstones) and was why the spirits were angry.
Answer: Ectoplasm.
Phixius ★