What is the ruling of Islamic law regarding marriage to a non-Muslim woman who had a relationship with a non-Muslim man, then recanted her desire to embrace Islam after having expressed it? And what is the ruling on a Muslim's attempt to warn her against returning to her former boyfriend?

It seems emotional matters have intertwined with issues of creed and religion for you. So, do not grieve over her, for she did not repent and returned to the forbidden with a disbeliever. Instead, ask Allah to grant you a believing, pious, chaste, and devout woman. A Muslim is committed to inviting non-Muslims to Islam without being lenient in addressing foreign women, and he should use indirect means in inviting them.