All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
The first marriage is void because the consent and presence of the Wali (guardian) are among the conditions for the validity of the marriage contract according to the preponderant opinion of the scholars; for more benefit on the conditions of the validity of marriage, please refer to Fatwa 83629.
Since this marriage is void, then that young man is not permitted to have sexual intercourse with that young woman and he is obliged to separate from her. However, the separation in this marriage should be by either the husband issuing divorce or that an Islamic judge invalidates the marriage, as we clarified in Fatwa 92478.
Then if this young man is not willing to renew the contract, this girl should submit her affair to Allaah and ask Him to facilitate for her a better husband. In case he did not consummate the marriage with her, she is not entitled to a dowry.
As regards the second marriage, if it took place while fulfilling those conditions [i.e. the conditions of a valid marriage contract], then it is a valid marriage. The fact that the first marriage was not made public and the like does not have any effect. Islamically, the husband is not obliged to inform his first wife of his second marriage as clarified in Fatwa 85948.
Finally, it should be noted that it is not permissible for a Muslim woman to have an affectionate relationship with a non-Mahram man as this involves much corruption. For more benefit, please refer to Fatwa 81356.
Allaah Knows best.