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 swearing a false oath by the Holy Quran?
Swearing a false oath by the Holy Quran dips the oath-taker in Hellfire, and one who had done so should turn to Allah in repentance, seek His forgiveness, give back rights to whom they belong, and pay the oath expiation.
I read the Qudsī ḥadīth: "Whoever breaks his wuḍūʾ and does not perform ablution has shown me harshness; whoever performs ablution and does not pray has shown me harshness; whoever prays and does not supplicate to Me has shown me harshness; and whoever supplicates to Me and I do not answer him, then I have been harsh to him, and I am not a harsh Lord." What is the authenticity of this ḥadīth?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
This ḥadīth was mentioned by al-Ṣaghānī (may Allah have mercy on him) in al-Mawḍūʿāt (p. 43), where he said: “Among them is their saying: ‘Whoever breaks his wuḍūʾ and does not perform ablution has shown me harshness; whoever performs ablution and does not pray has shown me harshness; (whoever prays and does not supplicate to Me has shown me harshness); and whoever supplicates to Me and I do not answer him, then I have been harsh to him, and I am not a harsh Lord.’”
Al-ʿAjlūnī (may Allah have mercy on him) cited what al-Ṣaghānī said in Kashf al-Khafāʾ (Vol.2/p.264). And Allah Almighty knows best.
What is the ruling on one who performs ablution or the ritual bath while having nail polish?
Nail polish must be removed before ablution or ritual bath so that water reaches what is beneath it, because it is a barrier that prevents water from reaching that area. This is based on the hadith narrated by Ali (may Allah be pleased with him) from the Prophet (peace be upon him): "Whoever leaves a hair's breadth of his body unwashed from major impurity, such and such will be done to him in the Fire." (Reported by al-Bukhari). And Allah the Almighty knows best.