Is it permissible for a person who hasn`t made ablution to call for prayer (Adhan)?
All perfect praise be to Allah, The Lord of The Worlds. It is disliked for a person with a minor impurity to call for prayer, but if he does , then it`s valid and sufficient. And Allah Knows Best.
What is the ruling on cheating to pass High School Exams?
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.
The Messenger of Allah said: "Whoever cheats, he/she isn`t one of us." [Moslim]. You should study hard in order to pass and excel. And Allah The Almighty Knows Best.
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.
Sometimes I receive a message containing a picture of someone desecrating the Noble Quran. The sender asks recipients to send that message to their contacts as an act of defending the Quran. What should I do when receiving such messages?
Praise be to Allah, the Lord of the Worlds.
You don`t have to circulate that message, because this isn`t the proper way to defend the Quran. And Allah The Almighty Knows Best.