What is the ruling of Islamic Law on someone who wakes up in a state of janābah (major ritual impurity) near the very end of the prayer's designated time, during cold weather — should he heat water in order to perform ghusl, even though the prayer's time will expire as a result, or should he perform tayammum instead?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If the water is cold, and cannot be used due to fear of harm that is not ordinarily tolerable, or that would result in illness, then in this case it becomes obligatory to heat the water — even if heating it causes the time for Fajr to expire — and no sin is incurred in doing so, due to his valid excuse. He may not resort to tayammum (dry ablution) instead, since water remains available [and merely needs to be heated].
Imam Shihāb ad-Dīn Aḥmad ar-Ramlī (raḥimahullāh) said: "He was asked regarding a person who, if he were to use cold water, would experience harm that permits tayammum, and who has access to something with which he could heat the water — but if he heats it, the prayer's time will expire. Is it obligatory for him to heat it even if the time expires, or should he pray with tayammum within the prescribed time? He answered that it is obligatory for him to heat the water, even if the time for that particular obligatory prayer expires." [Fatāwā ar-Ramlī, Vol.1/P.98]
Imam al-Bājūrī (raḥimahullāh) said in his Ḥāshiyah on Sharḥ Ibn Qāsim (Vol.1/P.173): "And if he fears [harm] from using cold water, and is currently unable to heat it, but knows of a place where firewood is available, such that if he were to go there he would not return until after the prescribed time has expired — what appears [to be the correct position] is that it is obligatory for him to go and seek the firewood, even if the time expires as a result, as this is the position ultimately settled upon by ar-Ramlī, and as related from him by Ibn Qāsim." And Allah, the Exalted, knows best.
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.
What is the ruling on praying in congregation at the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Congregational prayer (Salat al-Jama‘ah) is a communal obligation (Fard Kifayah) for resident men regarding the performance of the prescribed (obligatory) prayers. For men, praying in congregation at the mosque is better than praying elsewhere, such as at home. On the authority of Abdullah bin Umar, the Messenger of Allah ﷺ said: 'Prayer in congregation is twenty-seven degrees more excellent than the prayer of a person alone' (Reported by Bukhari & Muslim). Furthermore, on the authority of Abu Hurayrah, the Messenger of Allah ﷺ said: 'Shall I not tell you that by which Allah erases sins and raises ranks?' They said, 'Of course, O Messenger of Allah.' He said: 'Performing wudu thoroughly despite difficulties, taking many steps toward the mosques, and waiting for the next prayer after the prayer; that is your Ribat (steadfastness)' (Narrated by Muslim).
As for a woman, her praying in congregation at home is better for her than in the mosque, according to the saying of our Master the Prophet ﷺ: 'Do not prevent your women from attending the mosques, but their homes are better for them' (Narrated by Abu Dawood). Young boys should be encouraged to attend the mosques and congregational prayers so they may become accustomed to them. And Allah the Exalted knows best.
Do ear and nose drops break the fast?
Yes, ear and nose drops break the fast because both the nose and ears are open passages to the body cavity.