What is the recommended supplication (Du'a) upon breaking the fast, and is it recited before or after breaking it?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is recommended (Mustahabb) for a fasting person to recite upon breaking the fast—that is, immediately after eating or drinking—the supplication: "Allahumma laka sumtu wa 'ala rizqika aftartu" (O Allah, for You I have fasted, and with Your provision I have broken my fast).
This is because our master, the Prophet (peace and blessings be upon him), used to say this. The narration was recorded by Abu Dawud with a good (Hasan) chain of transmission, albeit in a Mursal form (a narration where a Successor reports directly from the Prophet). Shaykh al-Islam Imam Ibn Hajar al-Haytami (may Allah have mercy upon him) stated: "Its Mursal status is inconsequential, as it pertains to virtuous deeds (Fada'il); furthermore, it was connected (Mawsul) through another chain of transmission." [Tuhfat al-Muhtaj, Vol.3/P.425]
It is also recommended to recite: "Dhahaba al-dhama'u wa ibtallat al-'uruqu wa thabata al-ajru in sha' Allah" (The thirst has gone, the veins are moistened, and the reward is confirmed, if Allah wills).
This was recorded by Abu Dawud with a good (Hasan) chain. Our leading jurists (Imams) have explicitly stated that it is recommended for the fasting person to combine both supplications.
Imam al-Bajuri (may Allah have mercy upon him) stated:
"And his saying following his breaking of the fast—that is, it is recommended to say: 'O Allah, for You I have fasted, upon Your provision I have broken my fast, in You I have believed, to You I have submitted, and upon You I have relied. The thirst has gone, the veins are moistened, and the reward is confirmed, if Allah wills. O You of vast bounty, forgive me. Praise be to Allah Who aided me so that I fasted, and provided for me so that I broke my fast. O Allah, grant us success in fasting, enable us to stand in night prayer during it, and aid us in it while people sleep, and admit us to Paradise in peace.'" [Hashiyat al-Bajuri, Vol.1/P.562]
Furthermore, the fasting person may supplicate with whatever good he or she wishes, for the supplication of a fasting person is answered. Al-Bayhaqi recorded on the authority of Anas ibn Malik that the Messenger of Allah (peace and blessings be upon him) said: "Three supplications are not rejected: the supplication of a parent for his child, the supplication of a fasting person, and the supplication of a traveler." And Allah Almighty knows best.
How is the niṣāb (minimum threshold) of gold calculated when one owns gold of multiple different karats?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Zakāh is obligatory on cash and on gold designated for saving or for trade, provided the total reaches the niṣāb (minimum threshold liable for Zakah), and a full ḥawl (lunar year) has elapsed over it. The niṣāb is (85) grams of 24-karat gold; for 21-karat gold, the niṣāb equals (97) grams; and for 18-karat gold, it equals (113) grams.
If one owns gold of multiple different karats, the person paying zakāh should calculate the monetary value of all the gold he owns, combining these values together to determine whether the total reaches the niṣāb. He then pays zakāh on this combined monetary value, once the total reaches the niṣāb. The relied-upon position is to calculate the zakāh based on the buying price [i.e., the price the gold merchant would pay the owner to purchase the gold from him] on the day the zakāh obligation is due. And Allah, the Exalted, 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.
Is it permissible for a woman in her menstrual period to recite from the Mus-haf (copy of the Quran ), or to recite by heart?
A menstruating woman is permitted neither to recite nor to touch the Quran according to what Ali Bin Abi Talib (May Allah be pleased with him) reported about the Prophet (PBUH) who was only held from reciting the Holy Quran by Janabah (Major impurity) [Al-Tirmizi in a sound Hadith]. Although Janabah and menstruation are major impurities, a menstruating woman is permitted to supplicate Allah (Duaa`) and make Zikr (Tasbihat ), even if these involved saying words from the Holy Quran, provided that she does not mean the words for themselves but as a supplication, or Zikr. Moreover, she is rewarded for not reciting the Quran during her menstrual period because she abided by the injunctions of Allah.