Is it permissible for a woman to wear underwear while performing Umrah?
Yes, it is permissible for a woman to wear underwear while performing Umrah. This is because she should keep her regular clothes that cover all her body while being in a state of Ihram (ritual consecration) for Hajj, or Umrah. However, she should uncover her face and hands, but it is permissible for her to let her head-covering garment drape from her head down over her face when non-Mahram (i.e., marriageable) men pass by her. And Allah Knows Best.
What is the ruling on visiting a deceased's grave and supplicating Allah for him by his wife? Is the reward of reciting verses of the Holy Qur'an reaches the deceased?
There is no harm on visiting graveyard by woman with the intention of piety so long as they are dressed in accordance to the Islamic teachings. We ask Allah, The Almighty that the reward of reciting the Holy Qur'an on dedicated to the deceased reaches him. 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.
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.