There is a job opportunity in the Nuns Hospital. Is it allowed for me to take this job given the difficult living conditions and the high rate of unemployment?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

If your work is lawful and has no effect on your beliefs, then there is no sin on you and do your best to represent the true face of Islam. And Allah The Almighty Knows Best.

Is it permissible for a woman who broke fasting due to delivery to pay a ransom ?

She should make up for the missed fasting days once she becomes ritually pure, but it is impermissible for her to pay a ransom while being able to fast.

Should the Zakah(obligatory charity) giver tell the poor recipient that this is the Zakah of his money?

No, he shouldn`t. But, the Zakah giver should make an intention in his heart that it is the Zakah of his money when he gives it to the poor.

Is it permissible for one to give the Zakah(obligatory charity) to his indebted brother?

It is permissible for one to give the Zakah to his indebted , or poor brother.