Is it permissible to take out a usurious loan from a bank for construction, given that the questioner's current dwelling poses a danger to his and his family's lives, and there is no other way to build?

If remaining in the apartment poses a confirmed danger to you or your children, and you cannot rent another apartment, nor can you build with your own money, then it is permissible to borrow with interest (riba). This is because housing is one of the necessities without which life cannot be sustained, as Allah Almighty says: "And He has elaborated for you what He has forbidden to you, excepting that to which you are compelled." However, if it is possible to sell the current house and secure another dwelling with its price, then it is not permissible to borrow with interest, as the state of necessity would no longer exist.