Hello!
Bugs fixed! I was able to fix everything you said except your suggestion to not allow Katsune and Nana to see each other until you complete the rival quest. Nana's programming is not finished yet, I still have to think about how to introduce her in the story and give her a better routine, since at the moment she is only out of her room for an hour and, the rest of the time, she is in her room. So once I'm done working with it, the problem you mention will be solved!
Once again, thanks for your bug report!