Thanks for your response. But I don't think there is any item needed to be repaired. The bar at the top left corner cannot be fully green. I don't know if this is one of the bugs in the game.
#5 unlocks after you have fully upgraded your house with all the Carpentry (Bookshelf, Sofas etc) from the Carpenter Shop and maxed the Coziness (Green bar top left).
It is well worth it and beneficiary since you also get great food and Battle Cards from it.