Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
What is the ruling of Islamic Law regarding one who purchases a sacrificial animal (uḍḥiyah) and it then develops a defect before slaughter?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a defect that invalidates the sacrifice (uḍḥiyah) arises after its purchase — for example, if one purchased a sound, defect-free animal, and it then developed a limp, blindness in one eye, or a similar defect before slaughter — it does not fulfill the requirement of a valid uḍḥiyah, according to the Shāfi'ī school.
It is stated in Asnā al-Maṭālib fī Sharḥ Rawḍ al-Ṭālib (Vol.1/P.535): "Even if the limp develops [in the animal] while the knife is upon it, it still does not fulfill the requirement, because it is lame at the moment of slaughter — this is analogous to a case where a sheep's leg breaks and one hastens to slaughter it [in that condition]."
The Ḥanbalī school, however, held that if the one offering the sacrifice purchased the animal while it was sound and defect-free, and a defect then befell it afterward, the sacrifice remains valid and there is no obligation to replace it.
It is stated in Masā'il al-Imām Aḥmad, one of the Ḥanbalī reference works (Vol.8/P.4021): "I said: If a person purchases the sacrificial animal while it is sound, and it is then afflicted with illness, blindness in one eye, or a broken limb [before slaughter]? He [Imam Aḥmad] said: It is said that it still fulfills the requirement. Isḥāq said likewise, because he purchased it while sound, and the defect befell it only afterward, so it remains sufficient on his behalf." [End of quote]
Accordingly, a sheep afflicted with a defect that invalidates the sacrifice does not fulfill the requirement of a valid uḍḥiyah — whether the defect arose after purchase or during the slaughter itself — according to the Shāfi'ī school. However, there is no objection to following the Ḥanbalī position on this matter [as a valid alternative]. And Allah, the Most High, knows best.
Which is better for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.
What is the ruling on entering the toilet with something containing the remembrance of Allah?
It is disliked to bring into the toilet anything containing a reminder of Allah, such as the Quran or a sacred name (like the name of Allah, Muhammad, etc.). If one does that, etiquette dictates that he conceal it so it is not visible while entering the toilet, either by cupping his hands over it, putting it in his pocket, or inside his shirt if it is a necklace or ring. And Allah the Almighty knows best.
