Is the marriage, which lacks a valid legal contract, a guardian, and a court registration, valid?
It is incumbent that a valid marriage contract be concluded in the presence of a guardian and two trustful witnesses, and it should be registered in the court to protect the rights of the wife. Actually, a valid marriage contract is what differentiates between sound marriage and fornication.
Does touching one's wife invalidate ablution?
Touching the wife according to the Shafi'ee's doctrine invalidate husband's ablution. And Allah Knows Best.
Is Aqeeqah due on the miscarried embryo?
No Aqeeqah is due on the miscarried embryo.
Is a wife considered divorced if her husband refused to go to bed with her (for sexual intercourse) for two months?
A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.