Is it permissible for a Muslim woman to go out wearing adornment and not putting on her Hijjab(Islamic wear)?
It is impermissible for a Muslim woman to go out wearing adornment, and not having her Hijjab on.
Is it incumbent on a husband to pay the alimony of his wife if she had left him and stayed at her parent`s without his permission?
When a wife leaves her house, and stays at her parent`s without asking her husband, she is considered a Nashiz(wife who refuses to abide by her husband’s orders), and so she doesn`t deserve an alimony.
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.
Can the Christian widow whose husband is Muslim become an heir of his?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
A Christian widow can`t inherit her Muslim husband because their religions are different. And Allah the Almighty knows best.