How is night prayer offered?
Night prayer is offering voluntary prayer after Maghrib and before Fajr (Dawn). As for Tahajjud, it is offering voluntary prayer at night after waking up voluntarily, and for Allah`s sake as He Says (What means): "And pray in the small watches of the morning: (it would be) an additional prayer (or spiritual profit) for thee: soon will thy Lord raise thee to a Station of Praise and Glory!" [Al-Isra`/79]. Offering Tahajjud is better than offering voluntary prayer before going to bed.
Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the 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.