When does the time for Udhiyah begin?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The permissible timeframe for Udhiyah (sacrificial offering) begins on the day of Eid al-Adha—the 10th of Dhul-Hijjah—once the sun has risen and a period of time sufficient to perform two brief prayer units (Rak'ahs) and two short sermons (Khutbahs) has passed. This window remains open until the sun sets on the final day of Tashreeq, which is the 13th of Dhul-Hijjah.
Our Master, the Messenger of Allah (peace and blessings be upon him), said: "Every valley of Mina is a place of sacrifice, and slaughtering may be done throughout all the days of Tashreeq." (Narrated by Al-Bayhaqi and Ibn Hibban)
The days of Tashreeq refer to the 11th, 12th, and 13th of Dhul-Hijjah.
The most virtuous time to perform the sacrifice is immediately after concluding the Eid prayer, based on the statement of the Prophet (peace and blessings be upon him): "The first thing we do on this day of ours is to pray, then we return and offer our sacrifice. Whoever does that has acted in accordance with our Sunnah (tradition), and whoever slaughters before that, it is merely meat he has provided for his family; it has nothing to do with the ritual sacrifice." (Reported by Al-Bukhari and Muslim)
What is meant here is an estimation of time rather than the actual performance of the prayer itself, as our Master, the Messenger of Allah (peace and blessings be upon him), used to offer the Eid al-Adha prayer immediately after sunrise.
The sacrifice is valid if performed at any time during these designated days, whether by day or by night, though slaughtering at night is considered disliked (Makruh). And Allah the Almighty Knows Best.
If a woman becomes pure from menstruation before the Fajr Adhan in Ramadan, is she required to fast?
If a woman becomes pure (from menstrual period) before the Fajr Adhan, she must fast, as the impediment preventing her from fasting has been removed. The Sharia maxim in this regard states: "When the impediment is removed, the obligation returns."
She should then make the intention to fast before Fajr and perform ghusl (ritual purification) for prayer, whether before or after Fajr.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
What is the ruling on istinja' after urination, and is it done with water and soap or with water only?
Istinja' from urine and stool is obligatory. It is permissible to perform istinja' with water alone, or with toilet paper alone. The best way is with toilet paper then water. If one wishes to suffice with one of them, then water is better. And Allah the Almighty knows best.