What is the ruling of Islamic Law on a menstruating woman (ḥā'iḍ) reciting the Islamic ruqyah (Qur'anic/spiritual healing)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is permissible for a person in a state of janābah (major ritual impurity), or a menstruating woman (ḥā'iḍ), or a woman in postpartum bleeding (nufasā'), to recite for the purpose of ruqyah (spiritual/Qur'anic healing), even if this includes some verses of the Noble Qur'an — whether recited from memory or by looking at the Muṣ-ḥaf (the physical copy of the Qur'an) without touching or carrying it — provided that the intention behind the recitation is ruqyah, protection (taḥṣīn), and remembrance (dhikr), not the intention of tilāwah (Qur'anic recitation as an act of worship in itself). This remains permissible even if what is recited is an entire sūrah, such as Sūrat al-Mulk.
Imam al-Khaṭīb ash-Shirbīnī (raḥimahullāh) said: "It is lawful for a person in janābah to utter its [the Qur'an's] remembrances and other content — such as its admonitions, its narratives, and its rulings — so long as it is not with the intention of [reciting] Qur'an. [This is] like his saying upon mounting [a vehicle]: 'Glory be to Him Who has subjected this to us, and we could never have accomplished this [by ourselves]' [Sūrat az-Zukhruf: 13] — meaning, [could never have] been capable of it — or upon a calamity: 'Indeed we belong to Allah, and indeed to Him we shall return'... In fact, my teacher, ash-Shihāb ar-Ramlī, issued a fatwā that even if he recited the entire Qur'an without the intention of [reciting] Qur'an, it would be permissible." [Summarized from Mughnī al-Muḥtāj, Vol. 1/P.217] And Allah, the Exalted, knows best.
What is the ruling of Islamic Law on performing the Witr prayer after the Adhan for Fajr prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The time for Witr prayer begins after the ‘Ishā' prayer and ends with the rising of true dawn (al-fajr aṣ-ṣādiq). If a Muslim performs it at any point within this window, it counts as performed on time.
It is also recommended to make up a missed Witr prayer at any time — whether before or after performing the Fajr prayer, or at any other time of day. On the authority of Abū Sa‘īd al-Khudrī (raḍiyallāhu ‘anh), the Messenger of Allah ﷺ said: "Whoever falls asleep and misses the Witr prayer, or forgets it, let him pray it when he remembers, or when he wakes up." (Related by at-Tirmidhī)
Shaykh al-Islām, Imam Ibn Ḥajar al-Haytamī (raḥimahullāh), says: "The time for Witr prayer is between the ‘Ishā' prayer and the rising of dawn, based on the authentic ḥadīth to this effect. If this time has passed, it is permissible for him to make it up (qaḍā') afterward." [Tuḥfat al-Muḥtāj]. And Allah, the Exalted, knows best.
What is the ruling on one who performs ablution or the ritual bath while having nail polish?
Nail polish must be removed before ablution or ritual bath so that water reaches what is beneath it, because it is a barrier that prevents water from reaching that area. This is based on the hadith narrated by Ali (may Allah be pleased with him) from the Prophet (peace be upon him): "Whoever leaves a hair's breadth of his body unwashed from major impurity, such and such will be done to him in the Fire." (Reported by al-Bukhari). And Allah the Almighty knows best.
Is a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?
It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.