Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
What is the ruling of Sharia on looking at one`s Mahram women?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
A Mahram man (man impermissible for a woman to marry) is permitted to look at what usually appears from his Mahram women (women impermissible for a man to marry) while doing their daily housework, with the exception of their private parts. And Allah The Almighty Knows Best.
have an amount of 2,700 Jordanian dinars, which I have invested in a project, and I pay zakat on it every year. However, I have debts and obligations, and this project yields only a profit of about 2-4%. My salary is not enough to support myself and my family to the extent that I cannot pay the electricity bills. Is it permissible for me to take from the above Zakat?
You permitted to take from your Zakat since your income insufficient for you, because the poor is permitted to take from the Zakat in general, besides; the poor is identified of whose income doesn't suffice him. And Allah Knows Best.
In our region in southern Oman, specifically in the city of Taqah, there is a mosque that they say was built hundreds of years ago. This mosque is surrounded by graves, meaning it is in the middle and the graves are around it. People in our area differ, with some considering it permissible and others considering it forbidden to pray there. Moreover, my grandmother saw in a dream that she entered this mosque..."
Praying in this mosque is valid and and there is reprehensibility in its location so long as no grave exist within it. Besides, Sharia rulings aren't derived out of dreams. And Allah Knows Best.