Is it permissible for me to name my newborn baby boy “Al-Moustafa” ?
There is no harm in naming your son “Moustafa” without using the ”Al”.
What is the expiation for breaking fast due to being on a journey, or being sick, or being in a state of menstruation?
No expiation is due on the aforesaid categories, but they are obliged to make up for the missed fast. However, if any of them failed to do so while being able to, and the next Ramadhaan has come, then making up for those days is incumbent on him/her , and paying the ransom as well. And Allah Knows Best.
What should a mensurating woman, or in state of confinement do if she became ritually pure during the daytime of Ramadhan ?
If she became pure during the daytime of Ramadhaan, is desirable to complete her fasting during that day, and to make up for it along with other missed days due to menstruation. And Allah Knows Best.
A woman went for Hajj while pregnant, gave birth after leaving Arafat, and was unable to perform the Tawaf Al-Ifadah. If she cannot stay until she becomes pure from postpartum bleeding (Nifas) and she is from a distant country, what is she liable for?
This woman is advised to leave Mecca in a state of Ihram if the caravan departs. Once she reaches a distance where returning to Mecca is not feasible, she should consider herself in a state of being prevented (Muhsar). She may then exit Ihram, and she is required to offer a sacrificial animal (Blood) at that location. Additionally, she must perform a compensatory Hajj at the earliest possible opportunity. And Allah Almighty Knows Best.
