What is the ruling of Islamic Law on sitting between the two prostrations, and what is the ruling on the dhikr recited during it?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
Sitting between the two prostrations (al-jalsah bayna al-sajdatayn) is one of the pillars (arkān) of the prayer, while the dhikr recited during it is Sunnah according to the Shāfi'ī scholars. It is recommended (mustahabb) to say what was narrated from Ibn 'Abbās (may Allah be pleased with him), who said: "The Messenger of Allah (peace and blessings be upon him) used to say between the two prostrations in the night prayer: 'Rabbi ighfir lī, warhamnī, wajburnī, warzuqnī, warfa'nī' (My Lord, forgive me, have mercy on me, make good my deficiencies, provide for me, and raise me)." If one were to say a different supplication instead, such as "Rabbi ighfir lī" (My Lord, forgive me), the prayer would still be valid.
If the worshipper omits this dhikr between the two prostrations, whether intentionally or out of forgetfulness, their prayer remains valid and nothing is required of them, though they miss the reward of following the Sunnah. Leaving it out does not necessitate the prostration of forgetfulness (sujūd al-sahw).
It is stated in Hāshiyat al-Bājūrī 'alā Sharḥ Ibn Qāsim 'alā Matn Abī Shujā' (Vol.1/P.298): "The eleventh — i.e., of the eighteen pillars — his statement: 'sitting between the two prostrations,' meaning even in a supererogatory (nafl) prayer... his statement: 'with the supplication that has been narrated concerning it,' meaning: 'Rabbi ighfir lī, warhamnī, wajburnī, warfa'nī, warzuqnī, wahdinī, wa 'āfinī' (My Lord, forgive me, have mercy on me, make good my deficiencies, raise me, provide for me, guide me, and grant me well-being). Al-Ghazālī added: 'wa'fu 'annī' (and pardon me). Al-Mutawallī also added: 'Rabbi hab lī qalban taqiyyan, naqiyyan min al-shirk, bariyyan lā kāfiran wa lā shaqiyyan' (My Lord, grant me a heart that is God-fearing, pure from associating partners with You, innocent, neither disbelieving nor wretched)."And Allah, the Most High, knows best.
What is required of a traveler or a sick person if they broke their fast and then their excuse ceased?
If a traveler settles or a sick person recovers after having broken their fast, it is recommended for them to refrain from eating and drinking for the rest of the day, but it is not obligatory.
Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
What is the ruling on applying perfume while fasting?
Applying perfume does not break the fast. However, it is better to avoid it, as fasting is a practice of simplicity and restraint, while perfume is a form of luxury.