Is permissible to include a will requesting that a Holy Qur'an buried along with me?
It is not permissible to include a will requesting that a Quran be buried with the deceased in their grave. This is because the body of the deceased typically decomposes and may release impure substances, and it is not allowed to expose the Quran to impurity. Intentionally desecrating the Quran is an act of disbelief. Instead, read the Quran during your lifetime, as it will benefit you after death. And Allah Knows Best.
Is the `Iddah (waiting period) of the divorced effective from the time the divorce took place, or from the time of registering it at the court?
It is considered effective from the very moment her divorce took place, but not from the time of registering it at the court. And Allah Knows Best.
Is Aqeeqah due on the miscarried embryo?
No Aqeeqah is due on the miscarried embryo.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.