Is it permissible to swear upon the Book of Allah that what happened between me and my ex-fiancé is what I told him, knowing that I concealed some details, and is it better to stay away from the current suitor or to swear and return to being engaged to him?

This man's demand for you to admit to the forbidden acts you committed and his request for you to swear an oath to that effect is deviant behavior and contrary to Islamic law. You erred by informing him of some of the sins. The duty of someone who commits a sin is to repent and conceal their own transgression. We advise you to leave him if he persists in this demand. However, if you are in dire need of marrying him and he asks you to swear an oath on the Book of Allah, it is permissible for you to use ambiguity and equivocation in your oath by swearing that there were no forbidden acts between you and the man other than what you previously mentioned, and to inwardly intend what occurred after your repentance.