How is the Night Prayer (Qiyam al-Layl) performed?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Night Prayer (Qiyam al-Layl) refers to the voluntary (Nafl) prayers performed by a person after the Sunset prayer (Maghrib) and before the Dawn prayer (Fajr). As for Tahajjud, it is the voluntary prayer performed during the night specifically after waking up from sleep, as an act of devotion to Allah. Allah the Exalted says {what means}: "And from [part of] the night, pray with it [i.e., recitation] as additional worship for you." (Al-Isra/79). Thus, in terms of reward,Tahajjud is superior to voluntary prayers performed before sleeping. And Allah the Exalted knows best.
Does the 'aqīqah count as valid if it is slaughtered before the seventh day from the birth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The time during which it becomes permissible to slaughter the 'aqīqah begins from the moment the newborn is fully delivered from its mother's womb.
If the animal is slaughtered prior to the birth, it does not count as an 'aqīqah — it is simply considered an ordinary sheep slaughtered for its meat.
And Allah Almighty 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.
What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the Almighty knows best.