Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
Is it permissible for the heirs of the person who caused the accident (The Killer) to fast (The intended as an expiation for unintentional killing) on his behalf if the latter died in the crash?
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.
One who dies while liable for obligatory fast, his/her guardians have the choice to either fast on his/her behalf or feed one poor Muslim for each day of missed fast. This applies to Ramadan and other obligatory fast, and since expiatory fast is obligatory, feeding a poor person for each missed day or fasting on behalf of the deceased is obligatory as well. And Allah The Almighty Knows Best.
Are dream interpretation books accurate?
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.
Dream interpretation books are unreliable because they are merely expectations, not rulings of Sharia. However, if one sees a dream which one does not like, one should spit on one's left side and seek the refuge of Allah from the satan; it will not do one any harm, and one should not disclose it to anyone. If one sees a good vision, one should feel pleased but should not disclose it to anyone but whom one loves. And Allah The Almighty Knows Best.
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