Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.
Is Aqeeqah due on the miscarried embryo?
No Aqeeqah is due on the miscarried embryo.
When the soul leaves the body, does it hear and see? And where does the soul go?
The important thing is that the soul departs while its owner is a believing, repentant Muslim, as this is a good ending. As for the details, they are lengthy. The grave is either a garden from the gardens of Paradise or a pit from the pits of Hellfire. And Allah The Almighty Knows Best.
Is the Saum (Fasting) of someone who ate and drank forgetfully while offering fasting of oath expiation invalidated?
Whosoever eats, or drinks forgetfully is exempted by Allah; therefore, he/she shouldn`t break their fast whether it was obligatory, non-obligatory, or expiatory. And Allah Knows Best.