Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Does Istigfar (Asking Allah for forgiveness) between the first and the second part of Friday prayer`s sermon render the prayer invalid?
Talking during Friday prayer`s sermon is disliked, but there is no harm in offering Istigfar between the two parts of the sermon, and it doesn`t invalidate the prayer as it is actually from Sunnah. And Allah Knows Best.
A Christian woman wants to marry a Muslim man through an unregistered marriage contract and for a specific period because of certain circumstances. She is an adult and wants to know the correct procedure so as not to make any mistakes. What is the correct thing to do in this regard?
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.
Every marriage should be conducted through court in order to preserve the rights of the spouses and avoid any accusations. In fact, a person shouldn`t be ashamed of what is lawful. Rather, he/she should overcome those circumstances and start in the correct way. And Allah The Almighty Knows Best.
Is buying shared land from someone who has taken possession of it considered halal or haram?
The shared land is possessed by the country i.e. for all people; therefore, it shouldn't be possessed/occupied save by it's guardian/owner permission,thusly it can't be possessed save by having owners' permission. Finally, buying it from a person who don't possess it is impermissible. And Allah Knows Best.