To improve your relationship with the girls, the most important thing is to do their personal quests. As you do them, you will unlock more interactions with them, both sexual and everyday, such as eating and showering with them. At least once it's implemented, which will be soon.
Katsune, Fuyu, Yuri, and Kokoro's first personal quest is available at the end of Chapter 2 of the game, which is after completing the clubs story. This upcoming update 0.3 includes chapter 3 and when you complete it, you can do the first personal quest from the other main girls.
Your main story decisions serve to make them happier or angry, depending on which ones you make.
Currently, eating with them is useless. I have yet to add more utilities for this.
