Is Aqeeqah due on the miscarried embryo?

No Aqeeqah is due on the miscarried embryo.

Generally speaking, I`m dutiful to my mother and opt for obeying her. However, she chose a certain girl to be my future wife, but I`m not pleased with her choice although that girl comes from a good family and enjoys good character. Should I obey my mother or choose another girl that lives up to my expectations?

Praise be to Allah the Lord of the Worlds.

One must obey their parents in whatever is in compliance with the teachings of Sharia and within one`s capacity. However, you aren`t to blame for not marrying that girl, but it is better that you tell your mother about that and it is preferable that you perform Istikharah prayer. And Allah The Almighty Knows Best.

Is it permissible for the children of a deceased father to settle his debt from the Zakah (obligatory charity) money due on them?

It is impermissible to use the Zakah of one`s money for settling the debts of the deceased. However, children should settle the debts of their deceased parents out of filial piety. And Allah Knows Best.

What is the ruling on making up for missed fasting after the second half of Sha`ban (the month before Ramadhaan)?

One is obliged to make up for missed fasting before the start of next Ramadhaan, and regardless of offering it during the first, or the second half of Shab`an. This is because the prohibition mentioned in the Hadith is for offering absolute voluntary fasting in the second half of Sha`ban. And Allah Knows Best.