Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.
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.
Which takes precedence: the 'aqīqah or the uḍḥiyyah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is an act of worship through which a servant draws closer to Allah the Almighty in gratitude for the blessing of a newborn child. It is a confirmed Sunnah for those who are financially capable, and Allah does not burden any soul beyond what it can bear.
However, the uḍḥiyyah takes precedence, as it is a confirmed Sunnah established from the Prophet ﷺ through stronger and more numerous narrations — indeed, the Ḥanafī scholars hold it to be obligatory. Furthermore, its time is narrow and limited, expiring with the passing of the days of Eid, whereas the 'aqīqah may be delayed until one becomes financially capable of performing it.
And Allah Almighty knows best.
When is a child instructed to fast?
A child is instructed to fast at the age of seven if they are capable of fasting and have reached the age of discernment, by analogy to prayer. They should be encouraged but not forced, so they can become accustomed to it. It is obligatory for their guardian, whether a father or another, to instruct them.