Is it permissible for a woman to perform the obligatory prayer immediately after the adhan and before the Iqamah is performed in the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible for a woman to perform the obligatory (Fard) prayer immediately after the Adhan (call to prayer) and before the Iqamah (call to commence prayer) is performed in the mosque. And Allah the Exalted knows best.
What are the pillars of fasting?
The pillars of fasting are intention and abstaining from all nullifiers of fasting from dawn to sunset.
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.
Is it a condition that a woman should untie her locks while making Ghusl (ritual bath)?
Ghusl from Janabah (ritual impurity), or menstruation obligates that water reaches the roots of the hair in order for the Ghusl to be valid, but if it doesn`t, then hair locks must be untied for water to reach them, and for Ghusl to become valid.