Is fasting obligatory for a child?
Fasting is not obligatory for a child until they reach puberty. Puberty is determined by well-known signs, the most common of which are: nocturnal emission (for both males and females), menstruation (for females), or reaching the age of fifteen lunar years.
A guardian must instruct their children to fast once they reach the age of discernment, which is around seven years old, if they are capable of fasting.
Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?
It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.
Is Zakah (obligatory charity) due on the items used in the trading process such as: cars , shops etc..?
No Zakah is due on equipments used in the trading process such as cars and the like.
Is Fajr (dawn) Sunnah a confirmed one?
All praise be to Allah The Lord of The Worlds Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.