Is it permissible to listen to chants praising the Prophet if accompanied by musical instruments?
If singing, or chanting in praise of the Prophet was accompanied by a forbidden musical instrument, then it is forbidden.
Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
A young man who works for a conventional bank has proposed to me. Is it forbidden to marry him because he works there?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
Since the Messenger of Allah (PBUH) said: "When someone with whose religion and character you are satisfied asks your daughter in marriage, accede to his request. If you do not do so there will be temptation in the earth and extensive corruption."
Marrying such a person is permissible because he is a Muslim, and Allah may bless him with another job in which no usury/interest is involved. And Allah The Most Exalted Knows Best.
Is there zakat on social security savings (retirement benefits)?
If the retirement benefits are received, zakat is due on them for one year. Before receiving them, they are not in the person’s possession to be liable for zakat. And Allah Knows Best.