Hello! First of all, I'm SO SORRY it took me so long to reply to your feedback. I was heavily pregnant when I released this game and have since had my baby. I had a long and difficult recovery and it's hard to get around to anything with a newborn!
I combed through my coding to make sure things were triggering the way I had designed them and I wasn't able to find any issues upon inspection. Aya is designed to only get annoyed with you leaving if you open the game and close it again within about 5 minutes (this variable runs on an in-game time system, so it's not tied perfectly to your clock.) I've verified that this is working. This is to discourage people from opening her up just to check the gift shop and then closing her. Naturally, that would be distracting for her. You shouldn't be having long sessions with her and having her get annoyed at you leaving. If you think this is not the way it's working, it'd be massively helpful if you'd take a screenshot of the text you feel is triggering incorrectly and send it to ohunico.contact@gmail.com. If you are going to leave temporarily to take a break, you can always leave her open. You don't get penalized in terms of raising her distraction level, building resentment points, or triggering her 'annoyed' mood if you don't answer her when she asks you if you're still studying. That mechanic is there to prevent the player from leaving her open overnight to farm points for gifts. Again, she won't be any more distracted/resentful/annoyed with you if you just don't answer and reopen the game when you come back if it's closed.
All of your suggestions are honestly great. Unfortunately, with the way the saves work, it's very difficult for me to change or add major things to the game without corrupting everyone's save files and forcing everyone to restart, which I don't want to do. BUT I've already written your suggestions down and I will implement them if I ever do another game in this style, which is an idea I'm toying with c: I could definitely tweak her conversation when you come back after a while and she gets annoyed with your absence. I'll look into this and add it to her next update. You should get an alert here on itch every time she gets an update!
As for the gifts in the gift shop: they're all tied to her affection points except for the very last gift, which is tied to the easter egg event. You don't have to unlock all the previous gifts to unlock the last gift.