When is supplication (du‘a) more likely to be accepted: before or after breaking the fast in Ramadan?
Du‘a is accepted at all times, and this is part of Allah’s mercy and generosity toward His servants.
The Prophet ﷺ said: "No Muslim makes a supplication that does not involve sin or severing family ties except that Allah grants them one of three things: either He grants their supplication immediately, or He stores it for them in the Hereafter, or He averts from them an equivalent harm." [Narrated by Ahmad]
However, in Ramadan, du‘a is especially likely to be accepted shortly before breaking the fast.
The Prophet ﷺ said: "Three supplications are never rejected: the supplication of a fasting person until they break their fast, the supplication of a just leader, and the supplication of an oppressed person. Allah raises it above the clouds, opens the gates of heaven for it, and says: ‘By My might, I will surely grant you victory, even if after a while.’" [Narrated by Al-Tirmidhi]
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 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.