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).
How is night prayer offered?
Night prayer is offering voluntary prayer after Maghrib and before Fajr (Dawn). As for Tahajjud, it is offering voluntary prayer at night after waking up voluntarily, and for Allah`s sake as He Says (What means): "And pray in the small watches of the morning: (it would be) an additional prayer (or spiritual profit) for thee: soon will thy Lord raise thee to a Station of Praise and Glory!" [Al-Isra`/79]. Offering Tahajjud is better than offering voluntary prayer before going to bed.
Is a woman`s voice 'Awrah even when praising the Prophet (PBUH) via satellite channels?
Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The Sharia term 'Awrah has two meanings:-
First: `Awrah that invalidates prayer when uncovered, and in this sense a woman`s voice isn`t considered `awrah. Second: `Awrah that causes men to be tempted by women and vice versa. Moreover, if a woman`s voice is soft or alluring, then it is forbidden for her to speak deliberately before strange men. This is because Almighty Allah Says (What means): "O ye wives of the Prophet! Ye are not like any other women. If ye keep your duty (to Allah), then be not soft of speech, lest he in whose heart is a disease aspire (to you), but utter customary speech." [Al-Ahzab/32]. However, a man should avoid listening whatever incites his desires. And Allah The Almighty Knows Best.
Is it permissible to single out Fridays, Saturdays, and Sundays to make up for missed fasting without fasting a day before ,or after each ?
Yes, it is permissible to make up for missed fasting during the aforesaid days, and it is also valid to offer non-obligatory and vowed fasting as well. However, fasting a day before or after each isn`t obligatory. And Allah Knows Best.