What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?

Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.

Is it permissible to offer prayer at home, or should it be offered in the mosque?

All perfect praise be to Allah, The Lord of The Worlds.                                                                                                                                                                      It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. 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.

What is the ruling on aborting a fetus affected by thalassemia?