Should the Zakah (obligatory charity) giver tell the poor recipient that this is the Zakah of his money?
No, he shouldn`t. But, the Zakah giver should make an intention in his heart that it is the Zakah of his money when paying it to the poor. And Allah Knows Best.
Is it permissible to appoint a proxy for the sacrificial offering outside Jordan?
In the name of Allah; all praise is due to Allah, and peace and blessings be upon the Messenger of Allah.
It is permissible to appoint a proxy—whether an individual or a charitable organization—to perform the sacrificial slaughter (Udhiyah) on one’s behalf, even if it is carried out in a country other than that of the donor. This is conditional upon the proxy’s adherence to the established requirements of the Udhiyah, including the animal’s age, its freedom from physical defects, the designated timing of the slaughter, and the proper distribution of the meat.
However, it is preferable for the one offering the sacrifice to perform the slaughter personally, in order to attain the full reward and blessings of the act. And Allah (Exalted be He) 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]
Is it permissible to slaughter a sheep on Eid al-Adha with the intention of charity (sadaqah) on behalf of a sick person, and with the intention of udhiyah (sacrificial animal) at the same time?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The udhiyah (sacrificial animal) is an act of worship intended for its own sake; therefore, it must be slaughtered with the intention (niyyah) of udhiyah.
Whoever intends to draw closer to Allah through this act of obedience with the intention of udhiyah, and also intends to gift the reward to another person, there is no Islamic objection to that. And Allah Almighty knows best.