Lol, Well, each food item has a certain amount bytes and I think you can only eat 16 bytes a day. When you battle, the bytes change from a color to grey, meaning they have been eaten then once the slot is empty you can feed them more food until you reach the daily limit. Each food can give stat boosts like increasing your ATT, BRV, and HP. They also increase the sync rate, which is what increases the accuracy of your partner's fighting when in auto-battle.
The sync rate won't go up if you feed them food they don't like and they will tell you if they don't.
Lo, well, the Command system was partly inspired by TWEWY so :3 The music is amazing, and really everything in the game is perfect.
You select the [!!!] over Hachiko then you should change to a screen where you polish it. You might have to do something else before polishing it if that isn't hovering over it.
Oh, a good tip is to wait a few seconds without moving and you can talk to your partner. They usually provide tips on what you need to be doing.