Which is better in night prayer: long standing (Qiyam) or long prostration (Sujood)?
Long standing (Qiyam) is better in prayer. However, a Muslim should also observe tranquility and composure in their prayer.
Who is the one required to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered by the guardian of the newborn — the one upon whom the child's financial maintenance is obligatory — provided he is financially capable of doing so. 'Alī ibn Abī Ṭālib, may Allah be pleased with him, reported: "The Messenger of Allah ﷺ performed the 'aqīqah for al-Ḥasan with one sheep." — Narrated by al-Tirmidhī. And Allah 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.
What is the ruling on performing the Istikhara prayer after the Witr paryer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The Istikhara prayer (Prayer for seeking guidance) is a Sunnah. It consists of two units (rak’ahs) performed outside of the obligatory prayers, after which the person supplicates with the traditionally narrated du’a. It is permissible to perform it before or after the Witr prayer, as the Istikhara prayer is recommended at all times except during the disliked times—the periods in which prayer is prohibited. This is because its specific reason (the Istikhara and supplication) occurs after the prayer itself, and any prayer with a subsequent reason is not permitted during the prohibited times. It should be noted that the two rak’ahs of Istikhara are not fulfilled by performing only one rak’ah, nor by a prostration of recitation (Sajdat al-Tilawah), nor by a funeral prayer (Janazah). And Allah the Exalted knows best.