If someone regularly fasts the six days of Shawwal, are they obligated to fast them every year?
A person is not obligated to fast the six days of Shawwal every year, even if they have made it a habit. However, someone who regularly performs a good deed should not abandon it as long as they are able.
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 reciting the takbīr from Sūrat aḍ-Ḍuḥā to Sūrat an-Nās upon completing the recitation of the Qur'an (khatm)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is recommended to recite the takbīr from the beginning of Sūrat aḍ-Ḍuḥā through to the end of Sūrat an-Nās, and this is the recitation practice of the people of Makkah.
It is stated in Nihāyat az-Zayn (p. 65): "It is sunnah to begin each sūrah with the basmalah, since it constitutes a verse of it. It is also sunnah to say, before each sūrah — from aḍ-Ḍuḥā to the end of the Qur'an — 'Lā ilāha illallāh, wallāhu akbar' (There is no god but Allah, and Allah is the Greatest), based on what has been narrated regarding Imam ash-Shāfi‘ī (raḍiyallāhu ‘anh), who heard a man reciting this takbīr in prayer, and said to him: 'You have done well, and you have hit upon the sunnah.'"
And Allah, the Exalted, knows best.
Does using a respiratory device (oxygen) affect the validity of fasting?
Using an oxygen device does not affect the validity of fasting because oxygen is a gas with no physical substance.
However, if medicinal substances with physical particles are added to the oxygen, its use would break the fast, as it enters the body cavity through a natural passage.