Is it permissible for the woman who is observing Iddah after her husband`s death to sit with her daughter`s suitor, although their marriage contract hasn`t been concluded yet?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
A suitor who hasn`t concluded the marriage contract isn`t a Mahram*, so he must be treated as such. And Allah The Almighty Knows Best.
* The period a woman must observe after the death of her husband or after a divorce, during which she may not marry another man.
* In Islam, a mahram is a member of one's family with whom marriage would be considered haram, concealment purdah, or concealment of the body with hijab, is not obligatory; and with whom, if he is an adult male, she may be escorted during a journey, although an escort may not be obligatory.
Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
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 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.