What is the Islamic ruling on smearing the head of the newborn with the blood of the `Aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (makrūh) to smear the head of the newborn with the blood of the 'aqīqah, as this is a practice that belongs to the customs of the pre-Islamic era of ignorance (Jāhiliyyah). What is Sunnah instead is to anoint the newborn's head with saffron or another pleasant fragrance. And Allah Almighty knows best.
What is the ruling on offering a sheep as a sacrifice (Udhiyah) if its fat-tail is sound, except that when it was young, the tip of its fat-tail was cut so that it would grow larger? And what is the ruling in case of doubt regarding the amount that was cut?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Cutting a minor, insignificant portion from the tip of an animal's fat-tail (al-alyah) to encourage it to grow larger is not considered a defect, and it does not prevent the animal from being valid for sacrifice (Udhiyah).
It is stated in Tuhfat al-Muhtaj (Vol.9/P.352): "There is some scholarly deliberation regarding the common practice of cutting the tip of the fat-tail so that it grows larger. It could potentially be likened to a partial cut of the ear—supported by the jurists' general rule: 'even if it is a small amount.' On the other hand, if it is an exceptionally minor cut, it might have no effect on validity. This is explicitly clarified by the juristic exception to the general rule, which states that cutting a tiny piece from a large limb causes no harm. This latter view is more well-founded.
Furthermore, I found that some scholars investigated this matter and concluded: 'It should not affect validity if a custom-sanctioned portion of its fat-tail is removed during its youth to make it grow larger and look better, just as castrating a male animal causes no harm.' However, applying this unconditionally contradicts the established texts of the jurists, as understood from what I have laid out; thus, the restriction I specified is what must be relied upon."
Similarly, it is mentioned in Nihayat al-Muhtaj (8/135): "If a small piece is cut from the fat-tail to help it grow larger, the most well-founded view is that the sacrifice remains valid, as was given in a formal legal verdict (Fatwa) by my father [Shihab al-Din al-Ramli], may Allah be pleased with him. This is proven by the jurists' maxim: 'The loss of a tiny piece from a large limb causes no harm.'"
In cases where there is doubt as to whether the portion cut was large or small, the animal is still deemed valid for sacrifice. It is noted in Hashiyat al-Shubramallisi ‘ala Nihayat al-Muhtaj (Vol.8/P.135):
"This matter requires careful consideration, but the closer and more correct view is that it is valid. This is because soundness is the default state for the animal from which the piece was cut, and it aligns with what usually occurs—namely, that the part removed to help the fat-tail grow larger is naturally very small." And Allah the Almighty Knows Best.
What is the ruling if hemorrhoid blood exits after completing ablution?
If this blood is exiting from outside the anus (due to the hemorrhoid protruding), it does not invalidate ablution, because blood exiting from the body from other than the two orifices does not invalidate ablution. If it exits from the anus (meaning from inside it), it invalidates ablution, and one must perform istinja' from it, wash the area of impurity, and repeat the ablution.
However, if this blood exits continuously such that no time remains sufficient for purification and prayer without it flowing, then it takes the ruling of urinary incontinence (sals al-bawl). One then cleanses from it after the time for each prayer enters, performs ablution immediately thereafter, and performs the obligatory prayer immediately. There is no liability upon him after that if something of it flows, and he may pray as many voluntary prayers as he wishes. If he wants to pray another obligatory prayer, he must cleanse himself and perform ablution. And Allah the Almighty knows best.
Is it permissible to combine and shorten prayers at home before traveling?
It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.