Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.
A person prays in a certain spot within the rows of the mosque, and gets angry if someone else prayed at his spot. What is the ruling on this behavior?
All Perfect Praise be to Allah The Lord of The Worlds and may His Peace and blessings be upon our Prophet Muhammad and upon all of his family and companions Prophet Mohammad (PBUH) make it prohibited for a Muslim from having/taking a certain spot in the mosque when performing prayers if they arrived and find it occupied, furthermore; it is the religious duty on others (praying people) to offer a piece of advice to alert the ones who don't know, that whoever reaches a spot first at the mosque having a priority/privilege upon others in that spot. And Allah Knows Best.
What is the ruling of Islamic Law on continuity (muwalah) in the ritual bath?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Continuity (muwālāh) means washing each part of the body immediately after the previous one, without leaving a gap long enough for the first part to dry before the second is washed. According to the Shāfiʿī school, continuity is a recommended act (sunnah) in both the ritual bath (ghusl) and ablution (wuḍūʾ) — it is not obligatory.
It is stated in Nihāyat al-Muḥtāj ilā Sharḥ al-Minhāj: "Likewise, continuity in the ritual bath is recommended, just as it is in ablution."
Accordingly, continuity in the ritual bath is a sunnah. And Allah the Almighty knows best.
Is it permissible to give to the poor from among the People of the Book from the Udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to give to the poor among the People of the Book from a voluntary sacrifice (uḍḥiyyat taṭawwuʿ), just as it is permissible to give charity (ṣadaqah) to them. This opinion is a view (wajh) within the Shāfiʿī school, which was favored by al-Muḥibb al-Ṭabarī and Imam al-Nawawī. [See: Ḥāshiyat Ibn Qāsim al-ʿAbbādī ʿalā Tuḥfat al-Muḥtāj (Vol.9/P.365)]. And Allah Almighty knows best.