Is it permissible for a woman to take medication to regulate her menstrual cycle before marriage, and does it harm her health, and is the hymen broken only by the insertion of the penis or by the ejaculation of sperm?

It is better for a woman to avoid menstruation blockers, but there is no harm in using them for a legitimate reason, such as her approaching wedding. As for breaking the hymen, it occurs through vaginal penetration and not through the ejaculation of semen without insertion. It should not be broken by other means unless due to inability or other reasons, in which case there is no harm in removing it by an appropriate method.