Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.
What is the ruling on wiping the head during ablution from behind a barrier like a headscarf (hijab)?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. As for one who has a turban or headscarf on their head, it is permissible for them to wipe over it after wiping a part of their head in any place. This is easily done at the front of the head. This means the woman begins by wiping the front of her head from under the headscarf, then completes the wiping to the back of the head from over the headscarf. If the woman wipes over the headscarf on her head and the moisture reaches the scalp or some hair within the boundaries of the head, it suffices for wiping the head. And Allah the Almighty knows best.
What is the ruling on performing the Duha (forenoon) prayer before its time has begun, because I go to school early in the morning?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The Duha (forenoon) prayer is not valid if performed before its time has begun. Its time starts when the sun has risen to a noticeable height, that is, approximately fifteen minutes after sunrise, and it ends when the sun reaches its zenith (zawāl), shortly before the Dhuhr (noon) prayer. It is stated in Mughni al-Muhtaj (Vol.1/p.455): “Its time is from the rising of the sun [to a spear’s height] until the zenith.”
Accordingly, the Duha prayer is not valid if offered before the sun has risen, and its time remains open until just before Dhuhr. It may be performed at any time at school, during the break between classes or during recess. And Allah Almighty knows best.
Is it recommended (mustaḥabb) for the one offering a voluntary sacrifice (uḍḥiyyat taṭawwuʿ) to eat from its meat?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is highly recommended (Mustahabb) for the person offering a voluntary Udhiyah (sacrificial animal) to eat from its meat, but it is not an obligatory requirement (Wajib). Allah the Almighty says {what means}: "So eat of them and feed the needy who do not beg and the beggar. Thus have We subjected them to you that you may be grateful." (Al-Hajj/ 36)
"So eat of them": This directive is an encouraging recommendation, not a binding command.
The Qani’ (the needy who do not beg): Refers to a poor person who refrains from asking people for help out of dignity.
The Mu’tarr (the beggar): Refers to a poor person who explicitly asks others for assistance. And Allah the Almighty Knows Best.