Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram (unmarriageable) of hers.
What is the ruling on swimming while fasting?
Swimming while fasting is disliked (makruh) due to the risk of water entering the body cavity (jauf) through the nose, ears, or mouth, which would break the fast.
Ramadan is a month of tasbeeh (glorifying Allah), not Sibaha (swimming).
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.
Which is more excellent for a woman: to pray in the mosque or in her house?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Our Master the Prophet ﷺ said: 'It is more excellent for a woman to pray in her house than in her courtyard, and more excellent for her to pray in her private chamber than in her house.' Therefore, a woman’s adherence to her home and her refraining from going to the mosques—in obedience to the command of Allah the Exalted—attains a great reward and abundant recompense. Furthermore, women praying in congregation within their homes is better than their attendance at the mosques, based on the aforementioned Hadith. And Allah the Exalted knows best.