How should a person who is afflicted with continued major ritual impurity (incontinence of urine, bleeding outside the monthly period) perform ablution?
Such a person should make ablution for every prayer after its due time and after removing impurities from their body and outfit, and should place a fresh diaper whenever needed so as for the impurity not to spread out. They should also perform prayer immediately even if incontinence of urine continued, and should repeat the aforementioned for every obligatory prayer, then perform optional prayer as much as they want.
What is the ruling on a person in a state of major impurity (junub) or a menstruating woman (ha'id) reciting the Quran from memory?
It is not permissible for a menstruating woman, a postpartum woman, or a person in a state of major impurity to recite anything from the Quran, whether from memory, from the Quran, from a phone, or a computer. It is also not permissible for them to touch the Quran, based on what was reported from Ali bin Abi Talib that the Prophet (peace be upon him) was not prevented from anything regarding the Quran except major impurity (janabah). (Reported by al-Tirmidhi who said it is a hasan sahih hadith). Menstruation and postpartum bleeding are analogous to major impurity (janabah) as they are all major impurities (hadath akbar).
For those mentioned, it is permissible to mention Allah and supplicate even with verses from the Quran, provided they do not intend them as recitation of the Quran, but intend them as remembrance (dhikr) or supplication (du'a). And Allah the Almighty knows best.
Is it permissible to pay the Fitr Zakah (obligatory charity) of Ramadan on behalf of a dead person?
The Fitr Zakah of Ramadhaan isn`t due on one who had passed away before the sunset of the last day of Ramadan. And Allah Knows Best.
What is the ruling on performing istinja' with perfumed tissues or a tissue moistened with water?
Performing istinja' with perfumed or moistened tissues is not sufficient if they are not dry, due to the moisture on them reaching the impurity, which increases its spread rather than reducing it. Then, to remove the impurity, one must use pure water. And Allah the Almighty knows best.