1) Can a woman memorize Qur'an during her menses?2) If a woman has prolonged discharge and must make Wudu before every prayer, what is the most she go without making Wudu? Since she is allowed to prolong her prayer until the end of its time to keep the same Wudu for the next prayer, how long will she have to renew her Wudu? This would also go for Taraweeh and Juma'h prayer, must she make new Wudu during Taraweeh and for Juma'h. Does she need to make Wudu after the Khutbah even if the washroom is 4 flights down and she may miss prayer?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

A menstruating woman is not allowed to touch the Quran, to enter the mosque or to perform Tawaaf (circumambulation around the Ka’bah). Also, she has to stop performing prayers, fasting and having sex with her husband. But, she is allowed to recite from her memory whatever she memorizes of the Quran without touching it.

Al-Mustahaadah, a woman who has vaginal bleeding in between her ordinary periods, is allowed to read and touch the Quran, have sex, and perform Tawaaf. She has to perform the prayer and fast in Ramadan and she can do any form of optional worship.

Al-Mustahaadah is pure, but she has to perform ablution for every prayer just after the time of the prayer starts.
In such a case, a woman is allowed to delay the Thuhr prayer, for example, to its last time (i.e. a period of time during which one has time only to perform the present prayer before the time of the next one starts) and perform the 'Asr prayer just at the beginning of its fixed time. This, in fact, is called a nominal combination.

The Prophet instructed Hamna Bint Jahsh saying: “If you can, you may delay the Thuhr prayer to its last time and perform the 'Asr prayer at its start time and have Ghusl (ritual bath) when you become pure (from menstruation), but still bleeding, then perform Thuhr at its last time, and then, the 'Asr at its start time. Then, delay al-Maghrib prayer and pray al-Isha prayer as soon as its time starts and have Ghusl, and then, perform the two prayers in combination, then do so (as mentioned above).”

In addition, al-Mustahaadah is not allowed to perform two obligatory prayers in their two different times with one ablution unless she combines them as mentioned above. However, she is allowed to perform one obligatory prayer and whatever she wishes of optional prayers or to perform the Jumu'ah prayer and attend its Khutbah with one ablution.

Allah knows best.