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.
What is the ruling on someone who prays but does not fast, without a valid excuse?
Fasting is one of the pillars of Islam, and a Muslim's faith is incomplete if they neglect the obligation of fasting while being physically capable of observing it.
What is the ruling on ablution if vaginal discharge is expelled, and is it impure?
If these discharges exit from the external genitalia (apparent part of the vagina), they are not impure and do not invalidate ablution. If they exit from the internal part, they are impure and do invalidate ablution. If it is uncertain whether they are from the internal or external part, they are not impure and do not invalidate ablution.
The apparent part is what becomes visible when sitting, and what the husband's penis reaches during intercourse is considered part of the apparent. The internal part is what is beyond that. And Allah the Almighty knows best.
What is the age of the Aqiqa or the Udhiyah?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The minimum age for a sacrificial animal (Udhiyah) and the birth sacrifice (Aqiqa) is as follows:
Camels: Five years old, entering their sixth year.
Cattle and Goats: Two years old, entering their third year.
Sheep: One year old, entering their second year; however, it is permissible for a sheep to be six months old provided it is large in size and plump.
And Allah the Exalted knows best.