When does the time for the 'aqīqah lapse and pass?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the guardian was financially capable (mūsir) during the majority of the postnatal period (nifās) — which is sixty days — then the obligation of the 'aqīqah remains upon him until the child reaches the age of maturity (bulūgh). Once the child reaches maturity, the demand falls away from the father and those like him. At that point, it becomes Sunnah for the child himself to perform the 'aqīqah on his own behalf.
However, if the guardian was financially incapable (mu'sir) during the postnatal period, and then became financially capable after its expiry — that is, after sixty days — the 'aqīqah is no longer required of him. And Allah Almighty knows best.
What is the ruling on wiping the white area behind the ears instead of wiping the head?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. Wiping the white area behind the ears suffices for that. And Allah the almighty knows best.
Is it permissible for a woman who has become pure before the end of forty days of confinement to perform different acts of worship? and is it lawful for her husband to have sex with her?
Once postpartum bleeding ceases and she is certain that it won`t happen again, she becomes pure, and so she should perform Ghusl (ritual bath), pray, and fast. She can also have sex with her husband even before the end of (40) days because the minimum of postpartum bleeding is a moment, and the maximum is (60) days. However, the postpartum bleeding for the majority of women is (40) days, but this does not apply to rest of them.
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.