What is the ruling on Friday Ghusl (ritual bath)?
Friday Ghusl is a confirmed Sunna (Prophetic tradition) even if a person wasn`t in a state of Janbah (ritual impurity), or physically unclean. However, one who doesn`t make Ghusl on Friday isn`t sinful for the Prophet (PBUH) said: "It is good for a Muslim to make ablution for Friday prayer, but it is better to make Ghusul. [At-Tirmithi & Abu Dawood].
Is it permissible for a wife to boycott (not to attend to his different needs) her husband?
It isn`t permissible for the woman to boycott her husband unless he is the reason behind that, and it is recommended that both spouses seek the advice of righteous people to make reconciliation.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.
What is the ruling on memorizing the Quran during menstruation, knowing that I do not read directly from the Quran but from a paper or from my phone?
It is not permissible to memorize the Quran during menstruation because memorization requires repetition, and a menstruating woman cannot touch the physical pages of the Quran. Similarly, if the Quranic verses appear on the screen of the phone, it is considered like touching the Quran. And Allah Knows Best.