Is it obligatory to have an intention (niyyah) for every prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is obligatory for the worshiper to have a specific intention (Niyyah) for every prayer, meaning they must consciously intend the act of worship they are performing. The intention is a pillar (Rukn) of the prayer, and the prayer is not valid without it. It is not a requirement to utter the intention verbally; rather, doing so is considered a recommended Sunnah. And Allah the Exalted knows best.
What can a menstruating woman do on Laylat al-Qadr?
If a menstruating woman engages in remembrance of Allah (dhikr), supplication (du‘a), and sincere devotion, she has indeed observed Laylat al-Qadr. She may also listen to the Quran from audio sources such as the radio or television.
When does the time for Udhiyah begin?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The time for Udhiyah (sacrificial offering) begins once the sun has risen on the day of Eid al-Adha—which is the tenth of Dhul-Hijjah—and a period of time has passed equivalent to two brief prayer units (Raka'at) and two brief sermons (Khutbah). It then continues until the sunset of the last of the days of Tashreeq, which are the eleventh, twelfth, and thirteenth of Dhul-Hijjah.
The Prophet (peace be upon him) said: "All the mountain passes of Mina are places of sacrifice, and in all the days of Tashreeq there is slaughtering." [Narrated by Al-Bayhaqi and Ibn Hibban].
The best time to slaughter is after finishing the Eid prayer, due to the saying of the Prophet (peace be upon him):
"Indeed, the first thing we begin with on this day of ours is to pray, then we return and slaughter. Whoever does that has attained our Sunnah, and whoever slaughters before [the prayer], it is only meat he has presented to his family; it is not part of the ritual sacrifice (Nusuk) in any way." [ٌReported by Bukhari & Muslim].
It is valid to sacrifice at any time, whether by night or by day; however, it is disliked (Makruh) at night. And Allah the Almighty knows best.
Is it permissible for the person who hasn`t made wudu` (state of minor ritual impurity) to perform the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (Makruh) for a person in a state of minor ritual impurity (Hadath Asghar) to perform the Adhan. However, if he does so, his Adhan is considered valid and fulfills the sunnah of the Adhan despite it being disliked. And Allah the Exalted knows best.