What should someone do if they fasted for 30 days in their country, then traveled to a place where people are still fasting?
If a person completes 30 days of fasting in their country and then travels to another country where people are still fasting, they should continue fasting with them until they observe Eid. Even if they have already completed 30 days, he/she should abstain from eating and drinking and join the people of that country because he/she has now become part of that community.
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.
Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).
Is it permissible for a young man and a young woman to enter into a covenant as a married couple without having a true seclusion (Khalwah) until their marriage contract is officially concluded?
The relation which isn`t based on a marriage contract is forbidden, and entering into a covenant as a married couple is unaccounted for and is from the evil suggestions of the devil.