What is the ruling on eating or drinking during the first Adhan?
It is permissible to eat and drink during the first Adhan because it takes place before the break of dawn. The purpose of this Adhan is to notify Muslims of the approaching dawn so they can prepare to stop eating when they hear the second Adhan.
What is the ruling of Islamic Law on the prayer of zawal?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is recommended (sunnah) to pray four rakʿāt — either with a single tasleem or as two separate sets of two rakʿāt — immediately following the sun's decline from its zenith (zawāl). This prayer is distinct from the regular Sunnah prayer of Ẓuhr (sunnat al-ẓuhr al-rātibah), as explicitly stated by the Shāfiʿī jurists.
It is mentioned in Nihāyat al-Muḥtāj: "The prayer of zawāl is offered after the sun's decline — so were one to perform it before that, it would not count. It consists of two or four rakʿāt and is distinct from the Sunnah of Ẓuhr, as is evident from the fact that it is mentioned separately after the regular Sunnah prayers, and it becomes a make-up prayer (qaḍāʾ) if a long period of time passes by customary reckoning... Al-ʿAlqamī stated: 'Scholars refer to this as the Sunnah of Zawāl, and it is distinct from the four rakʿāt that constitute the Sunnah of Ẓuhr.' Our shaykh said: Al-Ḥāfiẓ al-ʿIrāqī stated that among those who explicitly affirmed its recommendation was al-Ghazālī in al-Iḥyāʾ, in the chapter on devotional litanies, noting that there is no tasleem between them — meaning there is no break between each pair of rakʿāt."
The time of the sun's decline (zawāl) marks the very beginning of the time for the Ẓuhr prayer.
And Allah the Almighty knows best.
"If the fidyah becomes obligatory upon a pregnant or nursing woman because she broke her fast out of fear for her child, is it obligatory from her own wealth, or from her husband's wealth?"
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The fidyah (ransom/compensation payment for breaking the fast) is obligatory from the wife's own wealth, and is not obligatory upon the husband unless he voluntarily chooses to pay it on her behalf.
It is stated in Mughnī al-Muḥtāj (Vol.2/P.174): "If the two [the pregnant woman and the nursing mother] fear for the child alone — such as a pregnant woman fearing miscarriage, or a nursing mother fearing that her milk supply would decrease, thereby endangering the child — then both the qaḍā' (making up the missed fast) and the fidyah become obligatory upon them, to be paid from their own wealth." And Allah, the Exalted, knows best.
Is Zakah (obligatory charity) due on leased property, and how is it calculated?
Zakah isn`t due on the leased property itself, but on the saved income from that property if it reached Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over saving it.