Is it permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.
Is it permissible to use unscented petroleum jelly (Vaseline) during ‘Umrah, in order to prevent skin chafing or irritation?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
According to the Shāfi‘ī school, it is permissible for someone in the state of iḥrām to use oils and creams free of perfume/fragrance on parts of the body other than the head and beard, for a genuine medical need — such as preventing skin chafing or irritation. However, applying them to the head or beard remains unlawful.
Shaykh al-Islām, Imam an-Nawawī (raḥimahullāh), says in al-Majmū‘ (Vol.7/P.279): "Oils are of two types: the first is an oil that is neither perfumed itself nor contains any perfume — such as olive oil, sesame oil, ghee, butter, walnut oil, almond oil, and similar oils. The use of this type is not unlawful anywhere on the body, except on the head and beard — where its use is unlawful without any disagreement [among the scholars]." And Allah, the Exalted, knows best.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
I work overtime after regular working hours and may become occupied with my phone or the work computer for personal matters — what is the ruling on this?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is obligatory upon an employee to abide by the instructions and regulations governing overtime hours, and equally obligatory to uphold honesty and avoid all forms of deception and dishonesty. Allah the Almighty says {what means}: "O you who have believed, be mindful of Allah and be with the truthful." [Al-Tawbah/ 119]
Whoever is assigned to work overtime must be present at his workplace — even if he has no specific tasks to carry out at that time. In such a case, he should strive as best he can to spend that time in a manner that benefits the institution he works for. If there is genuinely no work for him to do, there is no objection to occupying his time with something beneficial — such as reciting the Holy Qurʾān, reading, or listening to educational lessons — provided he has already completed all the responsibilities assigned to him.
If, however, he does have work to complete, he must spend that time fulfilling it. He may attend to phone calls or other personal matters to the extent that is customarily acceptable, as long as this does not result in delaying or postponing his work. If he delays his work on account of personal preoccupations, the wages he received for that wasted time are not lawfully his to keep, and he is obliged to return the equivalent amount to the institution by whatever means available to him. And Allah the Almighty knows best.