Is it permissible to have sexual relations with a European girl who does not adhere to any religion, without marriage? Can she be considered "that which your right hand possesses"? What is the legal ruling on that?

Adultery is one of the major sins, and its prohibition is known by necessity in religion. There is no difference in its ruling between a Muslim woman and a non-Muslim woman. The questioner must offer sincere repentance for getting to know this girl and living with her with the intention of committing adultery. He must cut off his relationship with her to prevent being drawn into something greater. It is not permissible to consider this woman a slave (milk yamin (definition)).