Question: Why is Beetlejuice so intent on marrying Lydia? Why not just find someone else?
Answer: If he marries a human, he can leave limbo and become human again. He needs to get away from his wife, who needs him to complete her blood ritual.
If he just wanted to marry a human, any human, he would not have waited for Lydia. He kept a picture of her on his desk.
Question: In the first movie, Beetlejuice worked with Juno, and later, Otho says that people who commit suicide become civil servants in the afterlife. In this movie, it's revealed that Beetlejuice didn't commit suicide but was murdered by being tricked into drinking poison by the woman he loved. Why would he be working in the afterlife if it was murder and not intentional suicide?
Answer: I thought the same thing on this and also why Lydia's husband was a civil worker, but there's a blink-and-you'll-miss-it part where Beetlejuice is reading a newspaper and there is a small story with a headline titled: 'Workers Wrongly Assigned Suicide at Death', which would explain it.
Question: "Little Jane" mentions that she and her daughter's Girl Scout troop agreed that their group Halloween costume would be "nothing Disney." Why does she not want any Disney costumes? Did I miss something?
Answer: It's not explained in the context of the movie. So you can only speculate. For example, they might want a theme to their costumes, or decided not to do Disney characters so there wouldn't be duplicate costumes. But in actuality, this moment is an inside joke for film nerds. Director Tim Burton had done several high-profile movies for Disney including the "Alice in Wonderland" and "Dumbo" reboots, and he's been pretty open about having a miserable time working with them due to their interference, control, etc. So the line was added as a bit of a jab at Disney, since Burton doesn't want to work with them anymore.
Question: Why doesn't anyone from the Afterlife try to stop Lydia from doing her TV series? In the first movie, Juno said that the living must not discover evidence of the Afterlife.
Answer: My guess would be that it's a combination of a few factors. The first is that she's far from the only one doing that sort of program. There are hundreds of paranormal shows, YouTube channels, etc. It would start to look very suspicious if suddenly things started happening to everyone who makes that type of content. Second, a lot of people just flat-out don't believe in things like ghosts and the afterlife. And a lot of those shows are faked, anyway. So while Lydia is earnest and honest, a lot of people won't believe it. Therefore, her show isn't exactly super risky for the afterlife. And finally, the original movie really doesn't dwell on that idea; it's basically given a few brief lines of dialogue in like one scene, and that's it. So you could also make the argument that this movie just sort of ret-conned or is ignoring that idea due to it being such a minor, unimportant element of the original.
Answer: I agree with Ted Stixon - many people have similar shows/online channels, and many people don't believe in the content. So, the afterlife officials are probably not concerned about all of them. There are people in real life who claim to be in contact with the deceased, as well as psychics and people with various religious beliefs.
Question: When Lydia needs to rescue Astrid and she calls on Beetlejuice, he appears and says, "The juice is loose." If he wants to be loose, why did he not appear this way before, when Rory called him? Instead of making Rory and Lydia enter the world of the model? (This also happened in the first movie - Adam and Barbara went to the model first.)
Answer: He's just making a joke by rhyming his name. I think you're reading too far into it.
I think you don't understand the actual question. It really has nothing to do with what he said, joking or not. For someone who wants out / wants freedom (disregard the joke), why did he not leave the model the first time someone (Rory) said his name? Instead of making Rory and Lydia enter the world of model the first time?
The scope of his power and influence seems relatively limited in the real world... almost exclusively confined to a small area around whichever ghosts (or strange and unusual humans) he's interacted with. Hence, him needing to perform the marriage ritual to escape the spirit world and be able to wage true havoc on the human world. So even if he left the model the first time, I doubt it would have ended up any different. Until Lydia agreed to marry him, all he could really do was just mess with her.
Answer: Why are most people so intent on marrying someone? He loves Lydia. In the first movie, she was a teenager, and he mostly needed a wedding to get out of his punishment. In the years since, he appears to have developed more respect and appreciation for her. He stopped her wedding to Roy, exposed Roy's fraud, and transformed their almost-wedding into the smaller, "private" ceremony that she really wanted. He doesn't want to "just find someone else" for the same reasons that many people don't.