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 the `Iddah (waiting period) of the divorced effective from the time the divorce took place, or from the time of registering it at the court?
It is considered effective from the very moment her divorce took place, but not from the time of registering it at the court. And Allah Knows Best.
What is the Islamic ruling when parents oblige their son or daughter to divorce or marry, and this actually takes place, although it is against their will?
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.
When the husband utters the word of divorce, without being forced or threatened, divorce takes place and we recommend that you visit the General Iftaa` Dept. to be given the suitable advice in this regard. And Allah The Almighty Knows Best.
What is the ruling on not offering prayer in a nearby mosque, and going to a distant one?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Praying in the nearby mosque takes precedence unless there was a circle of knowledge, or a larger congregation in the distant mosque provided that the congregational prayer in the nearby mosque isn`t undermined. And Allah Knows Best.