Does the property company have the right to allow the first floor owner to open the door and step on the steps to occupy the public area?

No right. According to the definition of * * * part and self-use part in the law and the contract between the two parties, the act of tearing down windows and changing doors and erecting steps without authorization encroaches on the * * * part of the house, which goes beyond the boundary of proper exercise of rights. Property management companies have no right to allow owners to occupy public areas, which is an infringement.