I appreciate you taking the time to write all this up! Gonna try and address each point best I can;
1. Thanks for pointing that out! I'll make sure it gets filed for updating (unfortunately, some higher priority projects are currently ongoing, so I can't say when that update will happen).
2. Copying the reply from another thread, but for both Favored Primordia and Metallic Shout, both those core bonuses are more narrative rather than hard mechanics: "For "rip and tear" its largely narrative! You might interpret it to mean that you now can rip through an enemy's armor or tear through a barrier. The exact effect is largely up to the table!" Those bonuses are more about setting up "fictional positioning" within the current situation vs some sort of stat bonus. They more directly benefit action rolls in that sense.
3. HP source being hard to find is definitely a known issue 😩 . Hopefully you were able to find the answer, but just in case, HP all comes from the Looks you have equipped.
For the play questions!
1. Looks (and enemies, and everything else that references a Tier) cap out at Tier 3! Though nothing is stopping you from going higher with Tiers if you wanted! The only major thing that would need tweaking would be some specific Token effects, but otherwise Looks and Enemies could just keep scaling up (I think).
2. Cash drops are high! Also like you pointed out, some builds (like the Flow stacker) can kind of break the game! That's pretty much working as intended. The LUMEN system that Vibe Check is running off of goes all in on the power fantasy, basically showering players in stuff. It's kind of the opposite of more "trad game" style of character progression. The sort of "philosophical goal" of most LUMEN games is to give the players the cool toys they want to play with upfront, and then see what happens!
3. This one's tricky! Players definitely can output a ton of damage very quickly when working together. You could try to throw some Bosses (using the templates) their way, to see if that changes anything, but also don't forget that on the GM Turn, you can also introduce more enemies! Additionally, there are other ways to create challenge outside of just enemy stats/density. Shifting the environment to become more dangerous or changing the mission type so that the players need to swap their tactics are good places to start. Also, are the players having fun wiping the floor with the enemies? Again, that kind of goes back to the wild power fantasy of LUMEN: lots of powerful toys. If the challenge aspect is really eating at you, I'd talk it over with your players and see what they think! If everyone agrees and wants more challenge, then bumping up enemy HP, decreasing cash drops (or increasing costs of everything instead) are fairly straightforward levels to adjust. If you're concerned about diagetically making those changes, well, maybe a Watcher isn't happy with how successful the Players have become and forces a reset!
4-6. This one kind of goes into the above response! If the players are having fun getting the cool loot, personally I don't necessarily see a drastic reason to change that, but if everyone wants more difficulty, then definitely adjust it! Every table is always going to be a little different in their goals. Also for the last part of 6, that concern does make sense! The intent of the random Tokens is to encourage players to always be trying out new strategies (and Looks). But if players are really wanting a specific Token and it just isn't coming up when rolling, then you can drop it in a store either to buy, or maybe as a side mission reward.
7. A little tongue in cheek, but they do do a lot of shopping in the TWEWY games 😆. But if you think that that doesn't make sense in your version of the Inversion, then absolutely change it! Could turn into an element of the narrative, like, maybe the shops are still open but the Players can't enter them. Now there's a new story hook to follow to see what has restricted their access!
TWEWY is also one of my favorite games of all time! Though I took inspiration from different elements, so the slower growth you're looking for isn't necessarily as hard-coded in Vibe Check. You mention that players effortlessly clearing the challenges isn't fun, and genuine question, are the players having fun doing that? It sounds like that no-challenge element is frustrating for you as the GM, which sucks! The GM needs to be having as much fun as the rest of the players! It's absolutely worth discussing this with your players to figure out the best way to adjust things so that everyone at the table is having fun.
I'm always happy to talk about ways to "tweak some game settings" so to speak!