Based on the above, this troper proposes that Billy died, woke up up in the Ghost Zone, hated it (among other things the other ghosts scared him) and couldn't stand being away from his adoring fans, so he escaped through the first natural portal he found, and high tailed it back to his mansion. That is assuming that ghosts form or otherwise start out in the Ghost Zone; if they don't then Billy probably hasn't been anywhere near the place (which might explain why he's bad at being a ghost).
WMG / Dude, That's My Ghost!
Ponzi's vendetta against Spencer is at least partly due to Spencer being related to BillyIn Ponzi's Got Talent we find out that Ponzi had his dreams pretty throughly crushed and was humiliated on television by a younger and still very alive Billy Joe Cobra when he went on that talent show. Ponzi would have definitely have held one hell of a grudge about that but would have been unable to do anything about it since there would have been no way for him to get at Billy. Then along comes Spencer who is pretty much a defenseless target and is related, albeit distantly, to the person who destroyed his dreams, making him the perfect substitute target for his ire, especially if the comment by one of the groupies in How To Impress Ladies wasn't just wishful thinking on their part and Spencer actually looks a bit like Billy.
The show is set in the same universe as Danny PhantomMost of Billy's powers match abilities possessed by ghosts in Danny Phantom (ie, shapeshifting, telekinesis, intangibility, invisibility, duplication, possession/overshadowing,etc) and the ones that don't aren't really any weirder than some of the one-off ghost powers in Danny Phantom. Additionally, Bobby is able to use ecto-blasts and in both shows ectoplasm can have weird effects on things, although the effects of ecto are rather more varied and dramatic in DTMG (maybe it's just a Billy thing). The 'can only be seen by someone wearing something that belonged to you' thing that Billy has and DP ghosts don't can be explained by Billy being bad at being a ghost (which is pretty much canon). Also Billy, Bobby, and Ghost-Spencer's colouring and general appearance aren't too dissimilar from that of some of the DP ghosts and most of the differences could be put down to the different art styles. Finally, both series have devices specifically to catch ghosts; the Fenton Thermos in Danny Phantom and the ghost containment device in Dude Thats My Ghost. Admittedly they seem to be somewhat different in how they work but that just means that there's more than one way to catch a ghost.
Madame X is Billy's sisterA bit far-fetched, this troper will admit, but that's the point of a WMG, right? A brother that she never got to see when he was alive, devoted her life to being a supportive fan, never was able to move on properly. They've got similar hair, and since that's all we've seen of her, it seems like enough to go off of.
Ponzi ghost-proofed his secret lair to catch BillyBased on the guess about Ponzi holding a grudge against Billy, it's possible that Ponzi hopes that Billy returned as a ghost so he can exact payback directly at Billy instead of settling for Spencer. That makes even funnier that, despite not knowing it, Ponzi once did get Billy locked in there.
The Wrights weren't the first family to live in Billy's mansionThey're distant relatives, after all, and would be lucky to get any piece of Billy's fortune, much less a Big Fancy House full of rock star memorabilia. The first people who inherited the mansion were closer on the family tree, but they somehow angered Billy. They probably tried to sell his stuff, the mansion, or generally disrespected it, and he couldn't stand it and haunted the hell out of them until they offloaded the mansion on the next set of relatives. Repeat ad nauseam until the Wright family came along. The Wrights don't seem to care about money as much as their hobbies and work, and never angered Billy to the point where he would actively attack them. In the episode where Spencer loses Billy's necklace and his stuff, the family is surprised when Billy starts haunting them, so he never attacked them before.