I'm a developer, so I'll leave it to others to answer more subjective questions, but hopefully the following info is helpful:
If people encounter major bugs when we release a new patch, we'll usually roll out a hotfix within several days to fix them, other smaller stuff will get fixed in the next major monthly patch. You can check the patch notes and read the "bug fixes" part of any of the updates posts for an example of the kind of issues you might expect to encounter. https://sadambober.itch.io/idol-manager/devlog
1. In the current beta version of the game, there are no "game over" screens. If you would go bankrupt (having a negative cash balance for too long), you'll get a message telling you that you've essentially lost the game, but the game will allow you to keep playing. (Though, when you have a negative cash balance, you're locked out of performing certain actions, so you may want to restart the game and try again if you run out of money.)
Our plan is to add multiple "endings," some of which are tied to gameplay (e.g. if you run out of money and the agency goes bankrupt, you get a story event with the investor who originally helped start the group) and some of which are tied to story bits (there is a "main story" that will have an eventual end point). We'll have a feature similar to the "one more turn..." button in Civilization games, where after the game "ends," you can choose to keep playing in what is essentially a sandbox mode.
2. There are "cheats" if you want to do things like give yourself money, unlock research stuff without having to spend research points, etc. See this thread, which also has a post from sadambober (co-developer) which also explains how you can manually edit your save files if you want to do things like edit an idol's stats: https://itch.io/t/339009/keyboard-shortcuts-and-cheats
3. In the next month or two we're planning to release the story editor, other modding tools will be released down the line but they're not our top development priority right now. Since mod tools were originally a Kickstarter stretch goal, we're prioritizing finishing the "base game" and some modding tools might come out post-release. (The reason we're releasing the story editor earlier is that it's something we're using as an internal development tool, so it doesn't require a ton of effort for us to package it and release it for players to experiment with.)
5. There is a "main story" that has events that are triggered when you hit certain milestones. There are also "side stories" that trigger when you hit specific criteria, which you may or may not encounter during a typical playthrough. (For example, there's a story event that triggers if you are spending a lot of time with a particular idol in a conspicuous way.) Some substories are "one shot" single scene events, while others might consist of several scenes that trigger across several days. (Also, during story segments you get to make dialog choices, and sometimes how long it takes for a substory to play out will depend on your choices.)
6. In the current version of the game, you have a "relationship" stat with each idol, which you can improve by socializing with them, or fulfilling requests for them (for example, maybe an idol wants to center at a concert). Dialog choices in substories also affect your relationship with idols. How good your "relationship" is with an idol affects things like how willing they are to share gossip with you (share information about who is secretly dating, who is getting bullied, etc).
With the next update, we're planning to expand the relationship system a bit, and instead of having a single "relationship" stat, split it into two separate stats: affection (how much the idol likes you) and influence (sort of a measure of how much they respect you). These stats are tracked separately, so it's possible to have influence with an idol even if she doesn't like you. If you have high enough influence you can force them to do things like stop bullying another idol, stop being friends with another idol, dump their current boyfriend/girlfriend, etc.
Right now idols can get into relationships with random people outside the agency or other idols (which can result in dating scandals), idols will be able to romance the player in future updates.
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Idols do graduate, every idol has a "natural" graduation date which you can learn by asking her about graduation when socializing with her, and you can also force them to graduate early (as a way of "firing" them without causing a public fuss). When they graduate, you can have the idol go out and recruit a successor (who will have similar stats), or have her become a staffer at the agency (e.g. dance coach, stylist, etc). After idols have graduated they'll show up on a list of graduated idols if you want to keep tabs on what they've been up to after leaving the group as a sort of mini-epilogue or "where are they now:"
7. Idols have two stats, physical stamina (drained by doing standard activities) and mental stamina (which can drain from things like bullying, being involved in a scandal, etc). Idols with low stamina can become injured (for low phys stamina) or depressed (low mental stamina) which results in a large penalty to all of their stats until they recover. Depression and low mental stamina can also be a trigger for specific substories (this is something that we'll continue to expand in future updates to add more variety). Suicide is a topic we'd like to explore in the finished game, but it's not yet part of the current beta.
Idols have their own interpersonal drama going on (they'll form cliques and may get into fights, which can cause their mental stamina to drain, and it's up to you to meet with the idols individually to find out who's bullying who, and so on; idols may not be willing to share gossip with you if you don't have a good relationship, and the bullying will happen and continue even if you choose to "ignore" it.
8. Idols' appearances are randomly generated with a random body, face, and hair style. There are 11 body types, 33 hair styles, and around 60 different faces. Whenever you hold an audition the game allows you to recruit up to 5 idols, and the game makes sure that every girl in the audition group has a different body/hair/face, though you might randomly similar-looking girls from different auditions. This part of the Kickstarter video might help give you an idea of the kind of visual variety you can expect, if you skip to around the 5-minute mark: (that being said, since creating the Kickstarter video we've added 2 new body types, 6 hair styles, and 12 faces, so the game in its current state actually offers a bit more variety than what is shown in the video. Also, certain things shown in the Kickstarter video have been reworked, like the concerts system).
9. If you download the itch.io client, you can use it as a launcher and the itch app will automatically download updates when they are released, sort of similar to how Steam works. You can download the itch.io app here: https://itch.io/app If you'd prefer not to download a separate app, you can also just download the game directly, but you'll have to download future updates manually.
10. The Kickstarter ended in April of 2018 (about a year ago), in July 2018 we launched an alpha that was exclusive to Kickstarter backers, before eventually transitioning into beta to allow people who weren't part of the Kickstarter campaign to participate and give feedback. Full game release date TBD but it will be some time later this year.
11. If you buy the beta on itch.io, you'll get a Steam key when the full game releases. When this happens, everyone will get a Steam key issued to their itch.io account, instructions for claiming your Steam key can be found here: https://itch.io/t/67604/how-to-get-a-steam-key-from-your-itchio-purchase (note that if you follow these instructions now, you won't find that button, because Steam keys haven't been issued yet).