Is it permissible to swear a false oath on the Qur’an that one will not associate with young men—with the exception of a suitor—in order to avoid losing him, knowing that there is a past history of relationships and a fear of scandal from one of them?

Lenience in intermingling and exchanging pictures between genders for the purpose of seeking a spouse is not permissible in Islamic law. This is one of the tricks of Satan, and you must make sincere repentance, cut off these relationships, and tell anyone who proposes marriage to approach the matter through its lawful channels. Know that the guardian was legislated for the wisdom of preserving and protecting the woman, and that the Muslim woman is modest and protected; she does not speak with non-mahram (definition) men except in a proper manner. And keep away from everything that is not lawful for you, and from anyone who digs into your past, and do not swear falsely. Remember that what has been decreed for you will come to you, and whoever abandues something for the sake of Allah, Allah will compensate him with something better. Occupy yourself with memorizing the Quran and with righteous company.