With Magical Harem Academy we have had some problems. First of all, we couldn't publish it on Steam because Steam threw it at us. And I don't program any of our 3D games, I pay a friend to program them. And, since the game does not generate income for us from Steam, and on Itch.io it generates very little, I cannot afford to pay you to continue developing that game, so we can no longer add new updates, so, if there are bugs, I'm afraid we can't do anything to fix them. Very sorry. Even so, we tested the game and were able to complete the chapter, so there should be no bugs that prevent you from doing so.
To advance the main story, let the first few days of the game progress until Kyomi comes to find you in your room. Then you will have to talk to a girl in the infirmary and, after waking her up with a potion, she will tell you what happened. Then she learns the spell that allows you to see the hidden and use it on a part of the dining room wall to make the dungeon door appear. Then you can go in and complete it.
What you mention about the feathers seems to be a bug. I'm going to download and test the game, see if I can get a love potion.
Intelligence and Popular points are earned by going to class. I don't know how many points there are exactly, but it shouldn't be many. Much encouragement!
Some girls are willing to have sex with you before others, such as Usagi and Neko, so you can have sex with them before the bar fills up. And yes, they can have sex with the female character too. Doesn't it let you have sex with them even when you've filled the entire bar?
I am very sorry that I cannot be of more help. If you need to ask me anything else, don't hesitate to ask. Thanks for playing!