Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
When does the time for Udhiyah begin?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The time for Udhiyah (sacrificial offering) begins once the sun has risen on the day of Eid al-Adha—which is the tenth of Dhul-Hijjah—and a period of time has passed equivalent to two brief prayer units (Raka'at) and two brief sermons (Khutbah). It then continues until the sunset of the last of the days of Tashreeq, which are the eleventh, twelfth, and thirteenth of Dhul-Hijjah.
The Prophet (peace be upon him) said: "All the mountain passes of Mina are places of sacrifice, and in all the days of Tashreeq there is slaughtering." [Narrated by Al-Bayhaqi and Ibn Hibban].
The best time to slaughter is after finishing the Eid prayer, due to the saying of the Prophet (peace be upon him):
"Indeed, the first thing we begin with on this day of ours is to pray, then we return and slaughter. Whoever does that has attained our Sunnah, and whoever slaughters before [the prayer], it is only meat he has presented to his family; it is not part of the ritual sacrifice (Nusuk) in any way." [ٌReported by Bukhari & Muslim].
It is valid to sacrifice at any time, whether by night or by day; however, it is disliked (Makruh) at night. And Allah the Almighty knows best.
Is it incumbent on the fiancée to obey her fiancé?
When the woman settles in her husband`s house, it is incumbent on him to provide for her and it is incumbent on her to obey him. Before that, and if the marriage contract had been concluded, then she is lawfully his wife and thus she should abide by custom in treating him, but if the marriage contract hadn`t been concluded, then she should treat him as a non-Mahram (Marriageable).
What is the ruling on performing Tarawih in sets of four rak‘ahs with only one Tasleem?
It is not permissible to combine more than two rak‘ahs with a single Tasleem in Tarawih prayer. Whoever does so, their prayer is invalid. Shaykh al-Islam Imam Muhammad al-Ramli (may Allah have mercy on him) stated: "If a person prays four rak‘ahs of the Tarawih prayer with a single Tasleem, it is not valid if they did so intentionally and with knowledge [of the prohibition]. Otherwise, it becomes an 'absolute voluntary prayer' (nafl mutlaq); because it is contrary to what has been prescribed." [Nihayat al-Muhtaj, Vol.2/P.127].