What is the ruling on performing Tahajjud after the Witr?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for one who has prayed the Witr to perform voluntary (Nafl) prayers after it. However, it is preferable for the Witr to be the final prayer of the night. Therefore, if a person is confident that they will wake up during the night for Tahajjud, it is recommended for them to delay the Witr until after the Tahajjud. Conversely, if one fears they may not wake up, they should perform the Witr before sleeping.
Al-Khatib al-Shirbini (may Allah have mercy on him) stated: 'It is not disliked (Makruh) to perform Tahajjud after the Witr, but it is not recommended to do so intentionally.' [Mughni al-Muhtaj, Vol. 1/P.454]. And Allah the Exalted knows best."
What is the ruling of Islamic Law on performing the Witr prayer after the Adhan for Fajr prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The time for Witr prayer begins after the ‘Ishā' prayer and ends with the rising of true dawn (al-fajr aṣ-ṣādiq). If a Muslim performs it at any point within this window, it counts as performed on time.
It is also recommended to make up a missed Witr prayer at any time — whether before or after performing the Fajr prayer, or at any other time of day. On the authority of Abū Sa‘īd al-Khudrī (raḍiyallāhu ‘anh), the Messenger of Allah ﷺ said: "Whoever falls asleep and misses the Witr prayer, or forgets it, let him pray it when he remembers, or when he wakes up." (Related by at-Tirmidhī)
Shaykh al-Islām, Imam Ibn Ḥajar al-Haytamī (raḥimahullāh), says: "The time for Witr prayer is between the ‘Ishā' prayer and the rising of dawn, based on the authentic ḥadīth to this effect. If this time has passed, it is permissible for him to make it up (qaḍā') afterward." [Tuḥfat al-Muḥtāj]. And Allah, the Exalted, knows best.
What is the ruling on wiping over socks?
It is not permissible to wipe over most common socks today because the conditions for wiping are not met. The concession was reported for wiping over leather socks (khuff) and socks (jowrab) with conditions: They must be thick, not allowing poured water to penetrate, enable one to walk in them, be worn while in a state of purity (from ablution), cover the entire foot up to the ankles (meaning covering the protruding ankle bones), and not be torn. And Allah the Almighty knows best.
Is it permissible for the wife to give the Zakah (obligatory charity) of her money to her poor husband?
Yes, it is permissible for the wife to give from the Zakah of her money to her poor husband. And Allah Knows Best.