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 is in her confinement to fast upon seeing blood signs that are neither black, nor red ?

Brownish, reddish, and yellowish discharges are all considered confinement until there is no colored discharge which marks the end of confinement. Moreover, the aforesaid woman is prohibited from fasting until she attains ritual purity. And Allah Knows Best.

Is it permissible for a sick person to pray while sitting on a chair?

All perfect praise be to Allah, The Lord of the Worlds                                                                                                                                                                        It is permissible for a sick person, who is unable to stand up, to offer prayer while sitting on a chair. If he/she was unable to prostrate while on the chair, the he/she should pray while sitting on the ground, but if he/she was neither able to bow (Roku),nor to prostrate, then he can do them while sitting on the chair. And Allah Knows Best.

Is keeping money in and taking profits from the Islamic Bank lawful? 

If Allah Wills this is lawful, because they stipulate on theselves to work in accordance to the guidlines of Islamic Law. And Alalh Knows Best.