A person vowed to slaughter a sacrificial animal. Is he permitted to eat from it?
If the vowed sacrificial animal was for the sake of Allah, and the one who vowed didn't specify then its meat should be distributed only among the poor and needy similar to distributing Zakah of Al-Fiter so neither him nor his dependents permitted to eat from; however if his vow was to made a banquet and invititing his relatives and others; then he must bring up as much as he can from its meat for them. In addition, he is permitted to eat from it in a reasonable basis. And Allah Knows Best.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
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.
Is it permissible to offer one Rak`ah in Witr prayer?
The minimum of Witr (An odd number prayer performed between Isha`a and Fajr) prayer is one Rak`ah, and the maximum is eleven, but the minimum of its complete form is three, and it is permissible to offer one only.