As a host you shouldn't be allowing guests to overstay for free or at all.
Part of being a host is learning how to be firm and professional.
It sounds like you haven't read through the Airbnb Help Centre to see how Airbnb works. Airbnb has liability insurance for hosts. If your guest needs to make a claim because of any injury in your home this can be used. Look it up in the help centre.
Just tell your guests they have to check out promptly and if they want to stay and you have room and want them to stay they can go into their booking and make an amendment to extend their stay.
Of course I am assuming if your brother rents the apartment that you have permission from your landlord to rent through Airbnb and you have taken out appropriate home insurance for short lets.
Airbnb is a business. I presume if you no longer want to use Airbnb you would sell the items you don't want or donate to charity.
EDIT
OMG Jennifer I just read your profile. You are not a parent to these guests you are a host in a professional business relationship with them. You don't need to provide them with icecream or pies. You shouldn't be cleaning up the bathroom after them or their dishes. Stop it.
And don't act as a left luggage facility.