What is the ruling on performing Umrah after the latest expansion of the Mas`aa (the passage between As-Safa and Al-Marwah), is it permissible, or not?
Yes, it is permissible to perform Umrah after the latest expansion of the Sa`y area since making Sa`y between As-Safa and Al- Marwah is already observed. And Allah Knows Best.
Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
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.
Is it permissible for a person who broke fasting in Ramadan because of being sick to pay a ransom?
If there is hope for him/her to be cured, then he would be required to make up for the missed fasting days when he/she recovers, and no ransom is due on him/her. If his/her disease is incurable, then he/she would be required to pay a ransom for each missed fasting day, which is (600) grams of wheat, or rice. And Allah Knows Best.