Is Aqeeqah due on the miscarried embryo?
No Aqeeqah is due on the dead embryo.
Is a woman`s neck an Awrah(private part)?
It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams(Marriageable men).
Is it permissible to swear by (Allah ”The Living”)?
Yes, it is permissible because “ The Living “ is one of Allah`s Attributes.
Is it permissible for a father to disinherit his disobedient, alcohol consuming son and his daughter who had fled home and never returned?
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.
It is permissible to give heirs some money because of their being extra obedient or needy. As far as inheritance is concerned, it is to be divided after one`s death, so it had better be left to the court itself. And Allah The Almighty Knows Best.