Does an internal examination require ghusl?
Ghusl isn't required for making internal examination; however, it invalidates one's fasting. And Allah Knows Best.
Is it permissible to fast on behalf of the dead who died owing missed fast to make up?
His relative should fast on his behalf, and it is permissible for the guardians to give permission to non-relatives of the dead to fast on his behalf as well. And Allah Knows Best.
Is it permissible to openly announce the engagement of a woman who is in her waiting period (iddah)?
It is not permissible to openly announce the engagement of a woman in her waiting period (Iddah), but it is permissible to hint (imply) at it if she is in her waiting period after the death of her husband. And Allah Knows Best.
What is the ruling on performing dry ablution (tayammum) on a wall or stone?
One of the conditions for tayammum is that it be with pure, clean dust (soil). It is not valid to perform tayammum by striking stones, a wall, sand that has no dust (i.e., that does not produce dust), pebbles alone, or clay, as these are not from the earth or its same category. And Allah the Almighty knows best.
