Is it permissible to offer Salah (prayer) on behalf of the sick who is on his/her death bed, and is incapable of offering it?
It`s impermissible to offer Salah on behalf of the sick, or the dead.
Is it permissible for me to eat from the animal that I slaughtered for Allah to protect my family?
It is permissible to eat from the non-vowed animal sacrifice, and the person is rewarded based on the amount of meat that he had given to the poor. However, there is no evidence in Islamic Sharia indicating that slaughtering an animal protects one`s family, but it is a way for thanking Allah, The Almighty, for his grace.
What is the Islamic ruling on adoption, and what is the legal window through which a person can be kind to an orphan girl, attend to her needs and raise her as his own?
Kindness to an orphan entails a great reward from Allah, but adoption is prohibited and invalid. Therefore, it is permissible for the aforementioned person (for example) to make his brother`s wife breastfeed that girl so that he becomes her uncle by suckling provided that he informs her that she isn`t his biological daughter.
Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.