Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?
The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.
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 amount of the Fitr Zakah (obligatory charity) of Ramadan?
The Fitr Zakah of Ramadhaan is a Sa` (2500 grams) from what the people of that country or state eat the most. And Allah Knows Best.
Does vomiting during the day in Ramadan break the fast?
Intentional vomiting is one of the nullifiers of fasting; whoever vomits deliberately breaks their fast.
However, if vomiting occurs involuntarily, the fast remains valid as long as nothing returns to the body cavity (jauf). If anything is swallowed back, the fast is invalidated.
The Prophet ﷺ said: "Whoever is overcome by vomiting does not have to make up the fast, but whoever induces vomiting deliberately must make it up." [Narrated by Abu Dawood and At-Tirmidhi]