The Dematerializer is functionally the same as in the live-action series.Specifically, its effects are permanent. The only reason the ghosts can come back so quickly is because Prime Evil has built a high-speed tunnel (the Scareway) between the dimensions. When the Ghostbusters' fathers did their thing, this tunnel did not exist, and ghosts had to wait for a hole to open up, resulting in a bottleneck effect. This tunnel can also open anywhere and anywhen, which is why the heroes need to time-travel.
The Ghostbusters are trying to protect the timeline.Prime Evil's trying to damage it, and the Ghostbusters don't really think about altering the timeline themselves: they show up, bust the ghost, and get out of there. Their costumes are equipped with perception filters and Translator Microbes, which accounts for just about every historical figure treating them without the least suspicion.
Tracy assisted Zero in the construction of the Dematerializer and other gadgets.Tracy seems to be "modified" in intelligence, so it's not implausible that Zero, the unseen boss in the 1970s show, did this and sent Tracy back into time. Why modify a gorilla, though? Why not just enlist a human being? There's an explanation in the '70s show: Tracy's animal side is just intact enough to render him (her?) immune to specific forms of magic—a witch's "glamour" leaves Spenser fooled but not Tracy. Zero must have figured that this would be useful in dealing with ghosts.
Lord Voldemort will become Prime Evil in the future.Assuming Voldemort isn't already dead, his dark magic will consume him one body part at a time. He will thus be forced to replace each part with a bit of machinery. If Voldy is already dead, then his spirit is inhabiting a skull and other assorted machinery. Also, having to lead a horde of nincompoop ghosts in a succession of take-over-the-human-world schemes and failing each and every time is the perfect Ironic Hell for him.
Possible explanations for the Haunted Castle/Mansion in the live-action series:
Eddie's mom is named Mable