Is it permissible for me to name my newborn baby boy “Al-Moustafa” ?
There is no harm in naming your son “Moustafa” without using the ”Al”.
Is Aqeeqah due on the miscarried embryo?
No Aqeeqah is due on the dead embryo.
Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram(unmarriageable) of hers.
What is the ruling on determining the sex of the baby whether through killing the female spermatozoa, or any other way in order to have a male?
If it is done through having a certain type of food, taking a certain type of medication, or organizing the time of the marital relation, then it is permissible.