What are the valid excuses for abstaining from congregational prayer in the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Concessions (Rukhsah) are granted to abstain from congregational prayer in the mosque due to general excuses, such as: rain that causes hardship in going out, strong winds at night, heavy mud that cannot be traversed without the risk of soiling oneself, hot winds, and extreme heat or cold. There are also specific individual excuses, such as: illness that makes walking as difficult as walking in the rain, severe drowsiness, evident hunger or thirst, the suppression of bodily wastes (urine, stool, or gas), and fear for one's life, limb, physical faculty, wealth, or honor, among other valid excuses. 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.
When does the time for the 'aqīqah lapse and pass?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the guardian was financially capable (mūsir) during the majority of the postnatal period (nifās) — which is sixty days — then the obligation of the 'aqīqah remains upon him until the child reaches the age of maturity (bulūgh). Once the child reaches maturity, the demand falls away from the father and those like him. At that point, it becomes Sunnah for the child himself to perform the 'aqīqah on his own behalf.
However, if the guardian was financially incapable (mu'sir) during the postnatal period, and then became financially capable after its expiry — that is, after sixty days — the 'aqīqah is no longer required of him. And Allah Almighty knows best.