Beetlejuice/WMG

Beetlejuice is the Tuxedo Kamen style Guardian of the Senshi of the star Betelgeuse
And Lydia is supposed to be Sailor Betelgeuse. It's kinda in the title this one. Obviously he got corrupted by Metallia for the film, but got better by the series.

Donny Juice was sent to Neither Neither Land at one point.
That's the reason he's so saccharine and sweet all the time. My guess is that he used to be a lot like his brother Beetlejuice, but eventually went one step too far with some stunt or another. One trip to the Jack In The Box later, and he's the Mister Rogers clone we all know and loathe. That's why Beetlejuice is so utterly terrified of Neither Neither Land. He's seen first hand what it can do to someone.

As a living child, Beetlejuice was Calvin
Think about it. They both love mischief, scamming people, have an affinity for striped clothing, they both have blond hair, and don't do well with authority. Beetlejuice loves puns, which he could have picked up as a child from his Saturday Morning Cartoon addiction.

As for why Beetlejuice's parents don't look like Calvin's parents, my guess is that Calvin died before they did. In their grief, Mrs. Calvin threw herself into her housecleaning, while Mr. Calvin did the same with working out, resulting in the ones we see in the show.

Hobbes (who turned out to be Real After All) was eaten by a Sandworm, and that's why Beetlejuice is so frightened of them despite having enough power to defeat them.

Cartoon!Beetlejuice is Lydia's Fairy Godparent
He has magic no other ghost seem to have, he's mostly focued on helping lydia and making her happy, he has the abillity to teleport and shapeshift while still having his prime colors own and usually flot. he's either pretending to be a ghost becuase he's afraid that Lydia thinks faries are lame, or he's suffering from some kind of amnesia

The show is a Prequel to the movie. Lydia and BJ just suffer from Laser-Guided Amnesia
Lydia looks a lot younger in the show then in the movie, and we've already seen that without BJ, Lydia will become very sad and depressed. It's not much of a stretch that without Lydia, BJ would become a bigger Jerkass. Sometime after the show ended, both Lydia and Beetle Juice got Laser-Guided Amnesia somehow and never met until Lydia and her parents moved to the Maitlands' house, where they met again (BJ now calling himself Betelgeuse), but they changed so much in the 4 years they never met, that they could never become friends again

The Maitlands' death scene was a false memory. Jane really wanted their house.
In the movie's afterlife, time moves quickly and the world makes a lot less sense. It would be pretty fair to say that reality is slightly off and subject to debate. The recently deceased are probably pretty confused and easily subjected to delusion. The zany slapstick death of Adam and Barbara is a fabrication they created to convince themselves someone they love didn't sabotage their car in order to collect from the sale on their house.

The Maitlands were infertile before they died.
Hence the look on Barbara's face and Jane's reaction of "I'm sorry I didn't mean it" when she says their house should be for a couple with a family.
 * It would also give further significance to Barbara's affinity for Lydia, and wanting to stay with her. "I like that little girl."