Which platform are you using, and which version of the game? Note that v0.3.0.1 is the latest which fixes a lot of problems such as crashes like what you described, so make sure you're using the latest files.
Hmm... that's an interesting issue, I (Rriik) have never run across it, but if it persists even after deleting and redownloading all the files it likely means it's related to the persistent data (saves, config files and the persistent dialogue history used for skipping). If you can open the game and look at the options menu, there should be a button to "Browse user data" which will open up the persistent directory. Try deleting the persistent.json file and restart the game, and let me know if it fixes the issue. (The folder location should be under "C:\Users\<user>\AppData\Roaming\Godot\app_userdata\Identity Visual Novel" in case you can't open it through the game).