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.
Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.
What is the ruling on eating or drinking forgetfully during the day in Ramadan or during voluntary fasting?
Whoever eats or drinks forgetfully while fasting, whether in an obligatory or voluntary fast, should continue their fast, for it is Allah who has provided them with food and drink. There is no difference between obligatory and voluntary fasting in this ruling.
The Jurisprudential Significance of the Ḥadīth: "Whoever says, at the conclusion of the Fajr Prayer, while crossing his legs, before speaking..."
"Whoever says, at the conclusion of the Fajr prayer, while crossing his legs, before speaking: 'Lā ilāha illā Allāh, waḥdahu lā sharīka lah, lahu al-mulku wa lahu al-ḥamdu yuḥyī wa yumītu wa huwa ʿalā kulli shayʾin qadīr' ten times — ten good deeds will be recorded for him, ten bad deeds will be erased from him, he will be raised ten levels, he will spend that day in protection from everything disliked and guarded from the devil, and no sin will be able to befall him on that day except associating partners with Allah" — does this noble ḥadīth apply to the imam, and what is meant by "extraneous speech"?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is recommended for both the imam and those praying behind him to recite, immediately after the final salām, the specific remembrance reported in the sunnah to be said before turning away from one's place of prayer. The imam then leaves his praying spot, and the act of "turning" is fulfilled when the imam faces the congregation — even without physically leaving his spot — by positioning his right side toward them and his left side toward the qiblah, and this applies even while he is engaged in supplication.
Al-ʿAllāmah Ibn Qāsim al-ʿAbbādī states in his Ḥāshiyah ʿalā al-Tuḥfah (Vol.2/P.105): "It is most virtuous for the imam, once he has given the salām, to rise from his place of prayer immediately afterward." He adds that an exception must be made for the remembrances that are specifically required to be recited before he turns away. He then notes, citing Sharḥ al-ʿUbāb: "Yes, an exception to this rising immediately after the salām applies to the Fajr prayer, due to the authentic report that the Prophet ﷺ, when he prayed Fajr, would remain seated until the sun rose." He further cites, from al-Khādim, the ḥadīth concerning one who recites, at the conclusion of the Fajr prayer while still in the position of crossing his leg to rise: "Lā ilāha illā Allāh, waḥdahu lā sharīka lah..." and the rest of the well-known ḥadīth. He comments that this makes explicit that this particular remembrance is to be recited before the worshipper turns his legs to leave, and the same applies to Maghrib and ʿAṣr, as reported in those contexts as well.
What is meant by "speech" in the relevant ḥadīth is extraneous worldly speech that is not called for after the prayer and for which there is no legitimate excuse. The remembrances reported to be recited upon concluding the prayer, however, do not fall under this category of extraneous speech, since they are themselves required by the sharīʿah.
Al-ʿAllāmah ʿAlī al-Shabrāmalsī states in his Ḥāshiyah ʿalā al-Nihāyah (Vol.1/P.551): "If someone greets a person with salām while he is occupied with reciting this remembrance [i.e., 'Lā ilāha illā Allāh...'], should he return the greeting — without this causing him to forfeit the promised reward, since he is engaged in an obligatory matter — or should he delay returning the greeting until he finishes, this being a legitimate excuse for the delay?" He continues: "I say: the more likely view is the former, and the prohibition on speech is to be understood as applying to extraneous speech for which there is no legitimate excuse. Based on this, should the worshipper give precedence to this remembrance ('Lā ilāha illā Allāh...') or to reciting Sūrat al-Ikhlāṣ ('Qul huwa Allāhu aḥad')? This requires consideration, though it is not unlikely that the remembrance takes precedence, given that the Lawgiver urged hastening to it through his words 'while crossing his leg.' This is not considered ordinary speech, since it is not extraneous to what is required after the prayer."
Accordingly, it is recommended for both the imam and those praying behind him to recite this remembrance and to give it precedence over the other remembrances of the prayer, ensuring it is said before they move from their place. And Allah the Almighty knows best.