Is Zakah due on a woman`s deposited gold?
Zakah (obligatory charity) is due on deposited gold if it reached Nissab (minimum amount liable for Zakah), and a lunar year had lapsed over owning it. The due Zakah is (2.5%). And Allah Knows Best.
Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
What is the ruling on a woman shaking hands with the brothers of her husband`s father, and not putting on Islamic wear before them?
The aforesaid are strangers to the their brother`s son`s wife, therefore, it is forbidden for her to take off her Islamic wear before them, or to shake hands with them.
Is the Aqeeqa due on the newborn in case of dying almost a month after the delivery?
Offering Aqeeqa after a week of a newborn death is recommended.