Not sure what you mean by special items... buuut...
All items that you can give to the girls are given to them in dialogue. You choose give item, then select it from the list. Never seen the cookbook, with over 70 hours in the game, but I'd assume it would transfer like all other stat books, just choose give item. You can only give two items per interaction then there is a 5 minute cooldown timer.
Items that add skills to the girls are placed directly in the "Skills" section of her character status card in the phone. You must have the item in your hero's personal inventory not in a storage box of the cooking tool's storage vault. You just click the "-----" line and then select the chosen item.
When a girl collapses from a cold or stomach flu, you have to give them cold or gastrointestinal medicine. You can do this through dialogue but instead of choosing give item, choose give medicine, then in the window click the little pill icon to switch from foods to drugs. Note, some foods also have similar properties and may help but do not work as well as medicine.
All tools and worn items are done in the character status card under equipment. Click the box next to the corresponding icon and select the tool/item you wish to equip her with.
Hope that helps your issue...
