PS: sorry for the wall of text.
First, I assume you're speaking about the black shirt you get after sharing insights with the Knight. For now, if i'm not wrong, she just wears it on very hot days. if you've gotten the item and gifted it to her, return home early from your adventure on very hot days and she should be using the shirt.
There is an item called Atsu Bozu, which guarantees a very hot next day when equipped but I haven't dropped it once.
Second, afaik there isn't a simple guide that points you towards stuff or gives you a walkthrough, but there is an official GoogleDoc with all events, items, effects and regions in the game. https://docs.google.com/spreadsheets/d/1fDTga-dhWarmZjoPLGN9X85UqCQwDj1L9NpInVcV...
Third, the answer is probably to look at the GoogleDoc, I myself am on day 57 and I still didn't see her brushing her teeth or just chilling in the tub since she always comes out first ( '-_-)
Fourth, tbh, it's easy to get bombs just by breaking every single vase and killing every enemy. the Salmon and King Salmon drop rates probably aren't that low, but since it's in a pool you basically roll a slot machine each time.
There are tips and ways to upgrade your character or give you some QoL, first way: Neko Plush Suit.
While it is a piece of equipment, it gives 10 weapon and 20 equipment inventory slots that "persist" after you remove the item. So if needed, you can switch one of your gears for the Plush Suit, get the items and switch it out. It's effectively an easy free inventory expansion, also locks your inventory to help not pick up useless gear from the ground.
Second way: Small Mana Gel. With Small Mana Gel you can upgrade your base weapon and equipment inventory, but the cost scales with each upgrade and there is no indicator that says how much is needed for the next upgrade. Obtainable from the breakable ores and from killing the Trash Bin on the main area after you've discarded some gears and weapons.
Third: The boss drop item, Philosopher's Stone Fragment. After you have healed Imouto, you can use the Philosopher's Stone Fragment on yourself, and it will heal you, increase your HP by a little and increasing your ATK by very little. The boss respawns every 7 days or every time the Tarot card 'The World' is used, getting progressively harder each respawn.
Edit: if you want to invest on getting Konpeito easier, don't buy the Konpeito with Salmon, give it to Aki (the shopkeeper) instead. She lowers the price for every Salmon you give her. It does take a while though.