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.
What is the ruling on a woman who takes medication to delay menstruation for fasting?
If a woman takes medication (to delay menstrual period) and does not experience menstruation, her fast is valid. However, she is not advised to do so unless there is a necessity.
If the medication harms her, even potentially, it is forbidden (haram) for her to take it.
What is the ruling on one who slept while firmly seated on the ground, regarding nullification of ablution?
The default ruling regarding sleep is that it nullifies ablution. An exception to this is one who slept while firmly seated on the ground; his ablution is not nullified by sleep if he wakes up while still firmly seated on the ground. And Allah the Almighty knows best.
What is the virtue of Laylat al-Qadr?
It is enough to know its great status that Allah revealed an entire surah about it—Surah Al-Qadr. Moreover, the Quran was first revealed on this night.
Allah says {what means}:
"We have indeed revealed this (Message) in the Night of Power: And what will explain to thee what the night of power is? The Night of Power is better than a thousand months. Therein come down the angels and the Spirit by Allah's permission, on every errand: Peace!... This until the rise of morn!" [Al-Qadr/1-5]
The Prophet ﷺ taught us to observe I‘tikaf in the last ten nights of Ramadan, seeking Laylat al-Qadr. Whoever worships Allah and revives this night will receive the reward of worshiping for a thousand months—excluding Laylat al-Qadr itself.