What is the ruling regarding the obligatory duties that a girl misses due to continuous bloody discharges for several days after the end of her menstrual period, resulting from ovarian dysfunction and polycystic ovaries? Do these duties become null and void, or must they be compensated for?

If the duration of the discharge, including the days of menstruation and purity, exceeds fifteen days, you are considered to be experiencing istihada (prolonged vaginal bleeding outside of menstruation). In this case, you should perform ghusl (definition) (ritual bath) after your regular menstrual period ends. You should then purify yourself and perform wudu (ablution) for each prayer after its time has begun, and you may pray as much as you wish with that wudu.

However, if the duration of the discharge, including the days of menstruation and purity, does not exceed fifteen days, then all of it is considered menstruation, and any intervening period of purity is valid. You should perform ghusl after the first cessation of blood. Then, if the blood returns, you are again considered menstruating, and if it ceases, you must perform ghusl again.

It is not permissible to delay prayer until its time has passed, whether you were menstruating and became pure, or if you are experiencing istihada. Ghusl is obligatory, or tayammum (definition) (dry ablution) if ghusl is not possible. You must make up any missed prayers along with repentance.