How many rak‘ahs are there in Tarawih prayer?
The most complete form of Tarawih prayer consists of twenty rak‘ahs, excluding Shaf‘ and Witr. This is the opinion of the majority of scholars, both past and present, and it is the practiced tradition in the two Holy Mosques.
However, Tarawih is valid with any even number of rak‘ahs, even two rak‘ahs, as long as it is performed with the intention of Qiyam al-Ramadan.
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.
Is it permissible to include others in the reward of one`s sacrifice?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for the person offering an Udhiyah (sacrificial offering) to include others in the spiritual reward of the sacrifice. However, it is not permissible for multiple people to jointly share the purchase price of a single sheep or goat, unless one person gifts the money to the other.
It is stated in Mughni al-Muhtaj (6/137) by Al-Khatib al-Shirbini:
"If a person includes someone else in the reward of his sacrifice and slaughters it on his own behalf, it is permissible."
It should be carefully noted that including someone else in the reward of one's sacrifice is completely distinct from offering a sacrifice on behalf of someone else. And Allah the Almighty Knows Best.
A man insulted the Divine Essence; is it obligatory for him to perform Ghusl?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Insulting or blaspheming the Divine Essence (Dhat al-Ilahiyyah) constitutes apostasy (Riddah). The perpetrator of this grave sin must immediately repeat the two testimonies of faith (Shahadah) and sincerely repent to Allah the Exalted. It is recommended (Sunnah) for them to perform a ritual bath (Ghusl), though it is not a mandatory condition [for the validity of their return to Islam]. And Allah the Exalted knows best.