Is it permissible for the man to go out wearing shorts?
All Perfect Praise is due to Allah, The Lord of The Worlds
It is permissible so long as his Awrah (private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed. And Allah Knows Best
Is it Permissible to lighten the eyebrows (I.e. Dye them blond)?
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.
Lightening the eyebrows is applying dye to them, and it is permissible to dye hair with other than black. The proof of this is the Hadith related by Muslim on the authority of Jabir told that when Abu Quhafa (Abu Bakr’s father) was brought on the day of the Conquest of Mecca with his head and beard white like hyssop, the Prophet (PBUH) said: "Change this with something, but avoid black."
However, it isn`t permissible for a Muslim woman to show her ornament (Zeenah) in the presence of non-Mahram men (Men permissible for a woman to marry). And Allah The Almighty Knows Best.
After buying tires, I made an oath not to buy tires from a person. Afterwards, he offered his entire car for sale. What is the ruling on this?
If you bought the entire car and in order to be on the safe side, you should pay an expiation; feeding 10 poor people and the cost of feeding a person is half a JD. And Allah Knows Best.
Although engaged to be married, a man committed adultery with another woman. What is the ruling of Sharia on this?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There is no sin on the woman to whom this man is engaged; however, he is considered a cheater and must receive the punishment prescribed in Sharia. And Allah The Almighty Knows Best.