Is it permissible for a menstruating woman to recite the Quran from the computer without actually touching the Quran?
It is not permissible for a woman in her menstrual period, or in postpartum to recite the Quran, even by heart, or without actually touching the Quran itself. Recitation itself is what is prohibited on her regardless of how it is done. However, it is permissible for her to surf through the Quran by her eyes, or to recall it in her head without uttering the words. There is no harm for her to look at the Quranic verses on the computer without touching it, or to utter the words as this is called looking not reciting or reading.
What is the ruling on Jumu‘ah (Friday) prayer for a traveler, and what are the conditions for it to be waived from him?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Jumu‘ah (Friday) prayer is not obligatory upon a traveler, whether on a long or short journey, provided that — according to the Shāfi‘ī school — he departs from his place of residence before the time for Fajr prayer begins, and that he does not intend to stay in the place he travels to for four days or more, excluding the day of arrival and the day of departure. If he intends to stay longer than that, he may not make use of the travel concession simply by arriving in that town. If he begins his journey after the adhān for Fajr has already been called, then Jumu‘ah prayer remains obligatory upon him, whether in his own town or in any town where Jumu‘ah is being held.
It is stated in Bushrā al-Karīm (Vol.1/p.383), from the books of the Shāfi‘ī school: "Jumu‘ah [prayer] is not obligatory upon a traveler on a permissible journey, whether long or short, if he departs from his place of residence before Fajr."
A "short journey" refers to travel covering a distance shorter than that of a long journey — that is, less than (81 km). The traveler begins to be entitled to travel concessions once he passes beyond the built-up limits of his town. And Allah, the Exalted, knows best.
What is the ruling on performing the standing (qiyām) and bowing (rukū‘) portions of the prayer normally, while performing the prostration (sujūd) seated due to knee pain?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If performing sujūd (prostration) in prayer causes the worshipper pain in the knees, then it is permissible for him to perform it through gesture (īmā') while seated, since Allah, Glorified and Exalted is He, has lifted hardship from His servants. On the authority of ‘Imrān ibn Ḥuṣayn (raḍiyallāhu ‘anh), he said: "I suffered from hemorrhoids, so I asked the Prophet ﷺ about [how to perform] the prayer, and he said: 'Pray standing; if you are unable, then sitting; and if you are unable, then on your side.'" [Ṣaḥīḥ al-Bukhārī]
If the valid excuse later subsides, the worshipper is then obligated to perform the prayer with all its pillars and conditions fully observed — including standing, rukū‘ (bowing), and sujūd (prostration). And Allah, the Exalted, knows best.
Is it permissible for a sick person to pray while sitting on a chair?
All perfect praise be to Allah, The Lord of the Worlds It is permissible for a sick person, who is unable to stand up, to offer prayer while sitting on a chair. If he/she was unable to prostrate while on the chair, the he/she should pray while sitting on the ground, but if he/she was neither able to bow (Roku),nor to prostrate, then he can do them while sitting on the chair. And Allah Knows Best.