Hi NissaRed, thanks for your interest in Idol Manager!
First off, I'll start by saying that the Kickstarter announcement video doesn't spoil anything related to the main story, and it may help answer some of your questions about the game, as it consists of a short "trailer" followed by a lengthier explanation of Idol Manager's gameplay systems. There is part of one scene that is briefly shown on screen during the video, but this scene is just one example of many optional substories that exist within Idol Manager, so hopefully it won't be spoiling too much. But if you'd like to avoid this part of the video, you can skip ahead to around 2:55 in the video. (If you choose to skip it, the voice-over for this part of the video says, "Idol Manager is a game with a strong narrative focus. However, rather than focusing on having a 'main' overarching story, most of the game is told through events and substories that will pop up as you play the game. There will be several narrative points that will be common to each playthrough, like the establishment of the agency, the introduction of a rival group, and some of the endings you'll encounter, but most of the narrative content is based on the events that happen with individual girls and staff members that you encounter during your playthrough.")
There isn't a fixed number of characters. Every time you hold an audition, the game will roll a set of idols that you can recruit. Each idol has a randomly-generated name, stats, and is assigned a trait and personality that will affect gameplay and partly determine the way she acts in story events. (There are a set number of faces, hair styles, outfits, and accessories that the game will choose from when generating an new idol. You can see examples of some of these in the video starting at around the 5-minute mark.)
It's hard to briefly summarize everything that's been implemented in terms of gameplay, but many of the game's core features and gameplay are described in the video, and you can check the devlog for information on the major features that we've added since entering beta: https://sadambober.itch.io/idol-manager/devlog
Certain parts of the story are still not fully implemented. This is partly because many substories are tied to gameplay mechanics that we're rolling out during monthly updates. For example, the most recent update added cliques, bullying, and fleshed out the relationship system more by giving you the ability to talk to idols and gossip about who's friends with who. This means that there were certain substories (tied to specific mechanics in the relationship system) that didn't get added until the most recent update. The final version will have a number of endings that aren't in the current version of the game, and throughout the game there will be several interactions with some of the "main characters" that are introduced at the start of the story; the intros and early interactions for these characters are included in the beta, but the later interactions will be added in future updates (some of them will be tied to specific gameplay milestones).
Most of the substories are intended to surface through specific gameplay interactions. Without spoiling too much, there are certain events that might only trigger if (for example) an idol has low mental stamina and becomes depressed, or if you begin dating someone and another idol becomes jealous. Because many of the substories have specific conditions to trigger, it's likely that you'll complete the game without seeing everything, and can explore more of the game's content by doing multiple playthroughs. But if you want to see all of the game's content, you'll probably have to choose a different playstyle for subsequent playthroughs; if you just do the same thing you did during your first playthrough, there's a good chance that you'll end up seeing some of the same events you saw during your first playthrough.
I hope that's helpful without being too vague.