Is it permissible for a teacher to inform her students at school about her private project of teaching English at her home, knowing that she will only accept graduated students, and would accepting students who have not graduated be considered an exploitation of her work?

If the school stipulates that staff members are not to deal with students in private lessons, then it is not permissible for you to advertise private lessons to your students, in fulfillment of the condition, for Allah Almighty says: "O you who have believed, fulfill [your] contracts." However, if the school does not stipulate this, then there is no harm in informing the female students about remedial lessons at your home outside of official working hours, whether you are the supervisor or another teacher, provided that a specific amount is determined for the fee and not a percentage, because the Prophet (peace be upon him) forbade hiring a worker until his wage is known.