What is the meaning of the Udhiyah?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The Udhiyah (Sacrificial Offering) refers to the livestock (An'am) that is slaughtered as an act of drawing closer to Allah the Almighty. This takes place on the day of Eid al-Adha (the 10th of Dhu al-Hijjah) and during the three days of Tashreeq that follow the day of Eid. And Allah the Exalted knows best.
What is the ruling of Islamic Law on a latecomer who joins the imam during the standing position of the first rakʿah but was unable to complete the recitation of al-Fātiḥah?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
If a latecomer (masbuq) joins the prayer while the imam is standing, he should begin reciting Sūrat al-Fātiḥah immediately, without pausing to recite the opening supplication (duʿāʾ al-istiftāḥ) or the seeking of refuge (taʿawwudh). If the imam bows before he completes al-Fātiḥah, he follows the imam into the bow and leaves whatever remains of al-Fātiḥah — the imam bears it on his behalf.
It is stated in ʿUmdat al-Sālik (p. 47): "If a latecomer finds the imam standing and is confident that he has enough time to recite the taʿawwudh and al-Fātiḥah in full, he may do so. If he is uncertain, he should neither recite the opening supplication nor the taʿawwudh, but rather begin directly with al-Fātiḥah. If the imam bows before he completes it, he follows him into the bow — provided he had not already begun the opening supplication or the taʿawwudh. If he had begun either of them, he continues reciting al-Fātiḥah for as long as he spent on them." And Allah the Almighty knows best.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
When does the time for the Fajr prayer begin?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The time for the Fajr prayer begins once the Mu’adhin starts the second Adhan (Al-Adhan al-Thani), and not after the first Adhan. And Allah the Exalted knows best.