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.
A group of about thirty young men will go to a farm on Friday. Is it permissible for one of us to deliver the sermon (*khuṭbah*) and lead us in the Friday prayer, or is it necessary to go to the nearest mosque?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The Friday prayer (Jumuʿah) is not obligatory upon a traveler, whether his journey is long or short, if he leaves his place of residence before the time of Fajr begins, according to the Shāfiʿī school. If, however, he sets out on his journey after the Fajr adhān, then he is obliged to perform the Friday prayer, whether in his own town or in any town where the Friday prayer is held.
It is stated in Bushrā al-Karīm (Vol.1/p.383), one of the books of the Shāfiʿī school: “[The Friday prayer] is not obligatory upon a traveler on a permissible journey, whether long or short, if he departs from his place of residence before dawn.” End quote.
Accordingly, if you set out on your journey after Fajr, you are obliged to perform the Friday prayer in the mosque. The same applies if you set out after that, since you would not have fulfilled the conditions for the validity of the Friday prayer, among them: that it be attended by forty men who are free, adult (bāligh), sane, and settled residents of the place where Friday is held. It must be held within a cluster of connected buildings, whether a city, a village, or a district (liwāʾ), for what counts is the gathering of the buildings. And Allah Almighty knows best.
What should one do if they see someone deliberately eating or drinking openly during Ramadan?
They must enjoin what is right and forbid what is wrong. If they fear harm from that person, they should disapprove of it in their heart but avoid sitting with them if possible. It is also preferable to seek the help of the authorities to prevent them from doing so.
What is the ruling on praying while wearing shoes?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
There is no sin for a Muslim to perform prayer while wearing their sandals or shoes, provided they are free from any impurities (najasa). It was narrated that Anas bin Malik (may Allah be pleased with him) was asked: 'Did the Prophet ﷺ pray in his sandals?' He replied: 'Yes.'" (Related by Al-Bukhari).
It is stated in Fath al-Bari (Vol.1/P.494) by Ibn Hajar (may Allah have mercy on him): "Regarding the phrase 'praying in his sandals,' Ibn Battal said: 'This is understood to apply as long as there is no impurity on them; furthermore, this is considered one of the legal concessions (rukhas)." And Allah the Almighty knows best.