1. Is one who pays Zakat based on an estimated end of the Hawl (Zakat year), without precise determination of its exact date, considered sinful? 2. What is the best option for paying Zakat among entrusting a sister to give it to a widow, or giving it to the mosque, or giving it to a divorced university student, or dividing it among them?

You must repent for any negligence in calculating and distributing Zakat, as Zakat is the right of the poor after the passing of a full year (Hawl). Attention must be paid to the difference between the Hijri and Gregorian years when calculating the Zakat Hawl. The general rule is that Zakat on wealth should be distributed in the country where the wealth is located. It is permissible to appoint someone to distribute it there, or to transfer it if the distance is less than that of a traveler's shortening of prayers (Qasr). It is permissible for your sister to give Zakat to the poor widow and her children to the extent of their basic needs, as the giving is due to poverty, not orphanhood. To identify a poor person eligible for Zakat, one should ascertain their condition personally, rely on trustworthy individuals' reports, or believe the needy person if their outward appearance does not contradict their claim. Even if it later turns out that they are wealthy, the Zakat would have been valid. This religion is one of ease, and one should feel content in worship and have good expectations of Allah.