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Summarized Fatawaa

Is it obligatory for someone traveling by plane in the afternoon during Ramadan to fast?

Anyone who intends to travel after dawn must begin the day fasting and continue with the intention of completing their fast, as fasting was obligatory upon them before traveling.
However, if they experience unbearable hardship after starting their journey, they are permitted to break their fast due to that hardship, not merely because of travel. In such a case, they must make up for the missed fast later.

What is the ruling on swallowing phlegm while fasting?

If a fasting person intentionally swallows phlegm, their fast is invalid, as it is possible to avoid it.
However, if they swallow it unintentionally, their fast remains valid.
Phlegm is impure and should be avoided.

Is it permissible to consume the meat of a sacrifice (Dhabihah) offered as an act of devotion to Allah, seeking His protection for my family?

Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
 
It is permissible to eat from this sacrifice, and the reward [for it] is according to what is given to the poor. And Allah the Exalted knows best.

Is it permissible to divide one mudd of fidyah between two people?

No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.