I'm aware retrospring is shutting down. I'll think about moving somewhere else later.
I believe you mean eating too much of the same food type would make Lilya more gluttonous (ie addicted) towards it. Unless I misspoke.
The main two food types are, broadly, meat and sweets. At the moment there isn't really anything that blurs the lines between them. There are things a little like eating pure sugar or grease though, in the form of weirder, fantasy food types that you will find in the setting. Stuff like creamy goop that's incredibly sweet, or raw slime. These are typically the more useful foods and grant unique, helpful states, but are very much more fattening than normal food items.
There could definitely be cases where a gluttony check tempts Lilya into eating even more decadent stuff she'd normally not consider, but that most likely wouldn't exist as normal items but instead would be part of a special event.

Depends on what you mean. I'll assume you're asking about randomness in regards to fetish content/weight gain and how it comes up in game.
There will be plenty of specifically placed traps and enemy encounters and such that are geared towards making Lilya fat or making her susceptible to gaining weight. But there will be a lot of random occurrences that can lead to weight gain as well. A random curse may turn out to be a fattening curse. A random trap may inflict a poison that makes Lilya eat more. When eating food or drinking potions, Lilya may be tempted into eating/drinking more which can have adverse effects. There will be various random events that can spontaneously happen, with good or bad results.
Primarily my goal is for the game to have a level of dynamism that often requires the player to react and deal with the unexpected pressures these random developments create, so RNG does play an important role in the structure of the game including the fetish content. Of course not much of it is 'pure' RNG, with either the chances being determined by Lilya's parameters, or depending on Lilya's skillset the player being able to counteract or prevent negative changes.
If there is concern about randomness gating content, most bespoke scenes especially with art will have specific triggers through either the story, quests, losing to certain enemies, or other things that can be done intentionally.

Very much delayed. Made a decision at the beginning of the year to recreate many of the systems from the ground up because many parts of it were getting annoying to work with or were just too limited and difficult to change, which would pose a problem for long term development. Mainly because of new scope on certain mechanics and a split with work on art this is taking a while. But this rebuilding is about 70% done I'd say and is in many ways in a better place than it was at the end of last year. I hope to make gamedev a larger priority soon as I want to get something out before the end of the year.
Demo, when out, will be Patreon exclusive for one month.