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.
What should I do in order to wake up for Fajr (dawn) prayer?
All perfect praise be to Allah, The Lord of The Worlds What should I do in order to wake up for Fajr (dawn) prayer? Answer: Some of the acts that aid in offering Fajr prayer are: 1- Going to bed early. 2- Willingness to wake up. 3- Reciting Al-Korsi verse from Chapter Al-Baqarah. 4- Taking refuge in Allah from the cursed devil, and making ablution immediatley after being awake, but it is preferable to ask someone to help in this regard to perform the Fajr prayer. 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 it permissible to participate in an Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Regarding the sacrificial offering (Udhiyah), if it is a sheep or a goat, it only avails for one person. However, if it is a cow or a camel, it avails for seven people. It is permissible for the seven participants to have different intentions; for example, some may intend the sacrifice (Udhiyah), some the ’Aqiqah (sacrifice for a newborn), and others may simply intend to obtain meat.
It is stated in Hashiyat Qalyubi ‘ala Sharh al-Mahalli (Vol.4/P.256) and in Bushra al-Karim (p. 706):
"If one slaughters a camel or a cow on behalf of seven... it is permissible. Likewise, it is permissible if some of them intend their seventh for meat, and others intend their seventh for ’Aqiqah." And Allah the Almighty knows best.