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 of Sharia on having an injection to stop the menses considering the fact that she is a challenged person?
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.
We recommend visiting a skilled doctor who fears Allah. If he says that there is no harm in having the injection, then it is permissible to use it. And Allah The Almighty Knows Best.
Should Al-Basmalah (i.e. saying Bismillaaahi Ar-Rahmaani Ar-Raheemi) be recited after Takbeerat Al-Ihram (saying Allahuakbar) which marks the beginning of prayer?
All perfect praise be to Allah,The Lord of The Worlds A praying person is obliged to recite Al-Basmalah at the beginning of Chapter Al-Faatihah, and in every Rak`ah (unit of prayer) because it is a verse of it. And Allah Knows Best.
What is the ruling on having a second congregational prayer in the mosque?
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 It is disliked to have a second congregational prayer in the mosque which isn`t visited by travelers like the neighborhood`s mosque, and which has an appointed Imam, save with the latter`s permission. Nevertheless, if the mosque is visited by travelers, it is permissible to have a second and a third congregational prayer, whether it has an appointed Imam or not, or whether he permits that or not. And Allah Knows Best.