Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
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.
Is it permissible to purchase the Udhiyah on installments?
It is permissible to purchase the sacrificial animal (uḍḥiyyah) on installments or by borrowing its price. However, it is not recommended for the poor to do so, because they are not required to offer a sacrifice, and Allah does not burden a soul beyond its capacity. If doing so would lead to negligence in providing for one's dependents (nafaqah wājibah), then giving precedence to obligatory maintenance over borrowing to buy the sacrifice is appropriate. This is based on the saying of the Prophet (peace and blessings be upon him): "It is sufficient sin for a person to withhold food from those whom he is responsible to support."
Furthermore, the sacrifice is valid from one who has a debt, but it is preferable (awlā) to repay the debt first, especially if the debt is due immediately (ḥāll). And Allah Almighty knows best.
How to perform the witr prayer in terms of connection (wasl) and separation (fasl)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The Witr prayer has several forms that vary in terms of virtue:
The First Form: Separating every two units (rak‘ah) with a Tashahhud and a Taslim (salutation). This is superior to connecting the units, even if it is only a single rak‘ah. This is based on the Hadith of ‘Aishah (may Allah be pleased with her): 'The Messenger of Allah ﷺ used to pray eleven units between the end of the ‘Isha prayer and dawn, performing the Taslim after every two units and performing Witr with a single unit.' (Related by al-Bukhari & Muslim).
The Second Form: Connecting the units with only one final Tashahhud at the very end.
The Third Form: Connecting with two Tashahhuds—meaning reciting the Tashahhud before the final unit without performing the Taslim, then standing to complete the final unit. This form is considered the lowest in rank so that the Witr prayer remains distinct from the obligatory Maghrib prayer, as stated in the Hadith: 'Do not make the Witr resemble the Maghrib prayer.' (Narrated by Al-Daraqutni, who stated its narrators are trustworthy).
It is stated in Bushra al-Karim Sharh al-Muqaddimah al-Hadramiyyah: 'It is permissible to connect [the Witr] with one Tashahhud in the final unit—which is better—or with two Tashahhuds in the last two units, as both methods are established in Sahih Muslim from the actions of the Prophet ﷺ. In the connected method, more than two Tashahhuds are prohibited. Furthermore, separating (al-Fasl) is better than connecting (al-Wasl) if the number of units is the same, because the Hadiths supporting it are more numerous and it involves more devotional actions.' And Allah the Exalted knows best."
