Is it permissible to shorten the eyebrows if they get too long?
Yes, it is permissible, but not desirable.
1- A young man whose father and grandfather are dead. Unfortuntly, he passedaway leaving a mother, two sisters and a brother. Do his paternal uncles inherit him? 2- A man died leaving daughters, a wife, brothers, a mother or no mother. It is well known that the daughters inherit two thirds and the wife one eighth. To whom does the rest of the estate go and what is the evidence on that from the texts of Sharia?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
1- The full brother or the paternal half-sibling disinherits the paternal uncles. The paternal half-sibling takes one sixth and because they are from the Asabah (Male relatives on the father`s side) of the deceased they take the rest of the estate. The proof of this is that Ibn ‘Abbas (May Allah Be Pleased with them) reported God’s Messenger (PBUH) as saying: "Give the shares to those who are entitled to them, and what remains over goes to the nearest male heir." [Agreed upon]. In this case, nothing is left to them.
2- The brothers take the rest of the deceased`s estate and the full brother disinherits the paternal half-sibling, and the proof of this is the aforementioned narration. And Allah The Almighty Knows Best.
Is it permissible for a man to propose to a woman during her `Iddah(waiting period)?
It is impermissible to propose to a woman in her `Iddah, but there is no harm in making an implication to such an end in case she was observing it due to the death of her husband.
If a disposable water bottle has the logo (Al-Aziz Water Shop) ,is it allowed to throw it away considering that (Al-Aziz) is one of Allah`s beautiful names?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
You can remove some of the letters so that the word isn`t read as (Al-Aziz). And Allah The Almighty Knows Best.