Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
Is it valid to share in the 'aqīqah by contributing a seventh share of a camel or cow?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible. If a group of people jointly share in the slaughter of a camel or a cow on behalf of seven individuals, this is valid — regardless of whether all of them intend the 'aqīqah, or some intend the 'aqīqah, others the uḍḥiyyah, and others simply the purchase of meat. And Allah Almighty knows best.
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.
Does nosebleed during the day in Ramadan affect the validity of fasting?
A nosebleed does not affect the validity of fasting unless some of the blood reaches the body cavity or the person intentionally swallows it. In such a case, their fast is invalid, and they must refrain from eating and drinking for the rest of the day and make up for that day later.