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.
What is the ruling on praying behind a disliked Imam?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is mildly disliked (Makruh Tanzihan) for a man—other than the permanent designated Imam (Imam Ratib)—to lead people in prayer if the majority of them dislike him due to a religiously blameworthy reason (Amr Madhmum Shar‘an), such as associating with open sinners (Fussaq), for example. As for the followers who dislike him, the prayer behind him is not disliked for them. However, if less than the majority dislike him, or if the majority dislike him for a reason that is not religiously blameworthy, then his leading the prayer is not disliked. And Allah the Exalted knows best.
What is the ruling on the ablution of one who touches his wife without a barrier?
In the Shafi'i school, a man's ablution is invalidated by touching his wife if their skins meet (in any place) without a barrier, whether the touch is intentional or accidental. An exception to this is touching hair, teeth, or nails; these do not invalidate ablution. And Allah the Almighty knows best.
What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the Almighty knows best.