Is it permissible to offer an Udhiyah on behalf of the deceased?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Offering a sacrifice (Udhiyah) on behalf of the deceased is permissible. This is the position of the Hanbalis [Kashshaf al-Qina’ by al-Bahuti (Vol.6/P.428)], and it was held by al-Abbadi of the Shafi’is [Bidayat al-Muhtaj by Ibn Qadi Shuhbah (Vol.4/P.358)]; it is also narrated from some Maliki and Hanafi scholars.
Abu Dawud included a chapter in his Sunan titled "Chapter: Offering the Sacrifice on Behalf of the Deceased," in which he narrated from Hanash, who said: "I saw Ali (may Allah be pleased with him) sacrificing two rams. I asked him, 'What is this?' He replied, 'The Messenger of Allah (peace be upon him) enjoined me to sacrifice on his behalf, so I am sacrificing on his behalf.'"
Abu Dawud also narrated from Jabir (may Allah be pleased with him) that the Prophet (peace be upon him) said: "O Allah, this is from You and for You, on behalf of Muhammad and his Ummah; in the name of Allah, and Allah is the Greatest," then he slaughtered it. It is well known that among the Ummah of Muhammad (peace be upon him) are those who have passed away, yet he (peace be upon him) dedicated it to his entire Ummah.
Furthermore, multiple Sharia texts have consistently indicated that the rewards of righteous deeds reach the deceased. This includes the permissibility of fasting on behalf of the deceased if they died owing fasts, as well as the permissibility of performing Hajj on their behalf, both of which are established in authentic Hadiths. Since the rewards for fasting—a physical act of worship—and Hajj—a physical and financial act of worship—reach the deceased, then the sacrifice (Udhiyah) is even more likely to reach them.
Moreover, the scholars have reached a consensus (Ijma') that the rewards of charities reach the deceased, and the Udhiyah is a form of charity and falls under its general category. Based on all of this, we hold the view that offering a sacrifice on behalf of the deceased is permissible. And Allah the Almighty knows best.
What is the ruling on reciting the Chapter after Al-Faatihah , and what should a worshiper who forgets it do?
All perfect praise be to Allah, The Lord of The Worlds. Any other part of Qur'an that a worshiper reads after Al-Faatihah during the first and the second Rak`ahs is a Sunnah, and forgetting to do so doesn`t nullify prayer, and doesn`t require performing Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
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.
Which is better during the day in Ramadan: reciting the Quran or performing voluntary prayers?
A Muslim should establish a daily schedule for reciting the Quran in Ramadan.
Once they have completed their daily portion (known as a wird or hizb), they can engage in other acts of worship, including voluntary prayers (nawafil). Prayer itself is called "Quran", because a significant part of it involves reciting the Quran.
Allah says: "BE CONSTANT in [thy] prayer from the time when the sun has passed its zenith till the darkness of night, and [be ever mindful of its] recitation at dawn: for, behold, the recitation [of prayer] at dawn is indeed witnessed [by all that is holy]." [Al-Isra`/78]
