Hey, I'm glad you're making this game. It definitely seems like a labor of love. I'm not usually into hypnosis, but I dabble occasionally, and this seemed interesting enough to check out. I'm glad I did!
I really like Dr. Faustus! She strikes a great, endearing balance between zany and welcoming. Her sharp but muted (dark?) character design really appeals to me. I'd describe her current content as "pleasantly relaxing", and would like to see more (and more varied!) content involving her!
On the other hand, the snake isn't quite my speed. I know there are plenty who would disagree; I imagine they could provide more helpful opinions. Regarding content warnings, when the player is about to make a decision that will enable potentially unwanted content, it might make sense to elaborate a little on just what they're getting into; you could probably do so without breaking immersion _too_ much. (Personally, it didn't really bother me, but I also generally don't get deep enough into trance to fall victim to that sort of thing... or at least, that's what I keep telling myself. ;P)
I found the pendulum and gem "minigames" to be somewhat distracting; that is, the mental effort they required to "solve" drew me out of my trance state and I ended up avoiding them entirely in the end. I can understand wanting to add a bit of variety to the game, though; I'm curious how you may end up experimenting with that goal in the future.
The subliminal message feature was a pleasant surprise. I think it would be useful to have separate controls for frequency and duration, and at some point support for custom phrase lists.
I think the game is definitely missing some kind of background sound. I think some combination of light trance music and/or simple tones/humming would be a good starting point when you get there; that said, I'm really discerning about sound, so I'd definitely prefer to be given the option to mute any background sounds if they're not to my liking.
On that note, I think some kind of basic pseudo-voiceover could be worth experimenting with. An approach like that can be cheap, flexible, and remarkably impactful when done with care. (For a high-profile example, see Undertale. :P)
Finally, I'd definitely like to see more character stills! Up to a point, the more variety you can provide, the more believable your characters will be, and the more they'll feel like people.
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Overall, you have a really solid foundation in a rare niche! I look forward to seeing more of your work; I hope my contribution helps! ;3
(PS: I recommend you try Hover or Namecheap to buy your domain, and Let's Encrypt for free and easy HTTPS to use with it! I can't recommend any hosting providers, that's outside my expertise.)