At least one more.
(but probably a whole lot more than one)
This is normal. The game is split into separate distributables in order to stay under the 2 gb limit. Since this is a kinetic novel, none of your choices affect the story.
Once you finish playing part 1, start part 2. After that, play part 3. Saves between the parts are incompatible (they are on different days), so just start a new game and select the "start" of that part.
The gallery and replay only has content for that part (otherwise it would eventually take up the entire 2 gb limit and leave no space for new story).
I am assuming you are on windows 11 using the itch launcher? Have you tried running the game outside of itch? tried running the game or the itch launcher in admin mode? tried installing it without the launcher?
I'm not familiar with the itch launcher, but these are standard steps when something complains about access issues.
You are free to think what you like, but some of these are intentional decisions and some others are incorrect.
1. The facial expressions are more natural and subtle than other games. The dev chose to not use exaggerated expressions.
2. Day 2 Lucy talks in the kitchen and upstairs, looking at the MC. If that isnt good enough, day 3 on the train we sit next to her and she looks directly at us.
3. This is another choice by the dev. He doesn't like random mouthflaps, so he decided to not make renders of characters mid-sentence with an open mouth.
4. Generally, the transition from a clean render to a messy render is done with a white flash. This is by no means the only game like this to use this technique. If you mean animations in the latest update, those appear to be normal speed.
5. There are only so many modifiers to work with in the modeling program, and fewer still if one doesn't want abominations. Assets and models can be somewhat limited.
The dev has posted some hairstyle change attempts on discord in the past. Unfortunately, a lot of the characters' looks are tied to their hair, and some look like entirely new characters when it gets changed. So I would not expect it too often.
One reason it works for Sarah is because we know she does cosplay and styles her hair for it, so we are conditioned to still recognize her.
I'm not saying it will never happen, just that for many girls it may be too big of a change to easily incorporate.
Have you played other Ren'Py games (many other visual novels)? I wonder if this is isolated to just Cosy Cafe, or Ren'Py in general. Checking my log file from a normal start, I see the same line about "Display Info: None", so that might not be the actual error.
However, on searching "renpy white screen crash" I found a renpy issue thread #6558 on github that mentioned this issue with NVidia xx60/xx70 cards running driver 576.xx or later. The NVidia tech mentioned that downgrading to 572.xx seemed to fix it, but personally that sounds more like a bandaid than a real fix. I didn't see a resolution for it in the thread. You mentioned being on a laptop, and it looks like you already tried to set Windows DPI/scaling to 100%. Did you try holding shift while opening the game to change renderers? Otherwise, I'm not really sure how to help.
Up until the last release, all the gallery items were included in part 2. However, if this trend was to continue the game would end up with no space in the 2gb APK for any new content, so the dev made the decision to cut out the replays and only include the ones from the specific days in the part. As it is, the content has grown large enough that the next update will be in a part 3, as the first two are filled up now.