Why was the exact date of Laylat al-Qadr concealed?
The wisdom behind this is to encourage Muslims to strive in worship throughout all the nights of Ramadan, or at least in the last ten nights. By doing so, they will earn the reward of observing Laylat al-Qadr as well as the reward of worshiping on other blessed nights.
Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
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 permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).