Rulings on the New-Born

Summarized Fatawaa

Is it permissible to swear by (Allah "The Living")?

Yes, it is permissible because "The Living" is one of Allah`s Attributes.

I used artificial nails on my wedding night, but I was surprised to find out that they require at least a week to remove. However, I performed all my prayers during that period. What is the ruling on those prayers?
 

If these nails prevent water from reaching one's skin then your prayer are invalid and obliged to redo all of them. And Allah Knows Best.

Is it permissible to abort a less than one-month-old fetus?

All perfect praise be to Allah the Lord of The Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Abortion is forbidden; therefore, it isn`t allowed except if endangers the life of the mother and such thing should be confirmed by god- fearing, specialized, trustworthy medical doctors. And Allah The Almighty Knows Best.

A man break his fast once during Ramadan and he already have an expiation of fasting for two consecutive months. He fasted for a month and passed away. Is it permissible for his sons to fast the remaining month equally? 

Fasting for expiation must be performed consecutively. I advise his children to feed sixty poor people, giving each one half a kilogram of rice or its monetary equivalent. This is because if a living person is unable to fast, they are required to feed sixty poor people, and death constitutes an inability. And Allah The  Almighty Knows Best.