What is the ruling on someone who eats or drinks thinking that the night is still present, then realizes that dawn has broken?
Whoever eats or drinks thinking that the night is still present, then later discovers that dawn has broken, must refrain from eating and drinking for the rest of the day out of respect for the sacred month. However, they must make up that day after Ramadan, and there is no sin upon them.
Is it permissible to pay the Fitr Zakah (obligatory charity) of Ramadan on behalf of a dead person?
The Fitr Zakah of Ramadhaan isn`t due on one who had passed away before the sunset of the last day of Ramadan. And Allah Knows Best.
Is it permissible to participate in an Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Regarding the sacrificial offering (Udhiyah), if it is a sheep or a goat, it only avails for one person. However, if it is a cow or a camel, it avails for seven people. It is permissible for the seven participants to have different intentions; for example, some may intend the sacrifice (Udhiyah), some the ’Aqiqah (sacrifice for a newborn), and others may simply intend to obtain meat.
It is stated in Hashiyat Qalyubi ‘ala Sharh al-Mahalli (Vol.4/P.256) and in Bushra al-Karim (p. 706):
"If one slaughters a camel or a cow on behalf of seven... it is permissible. Likewise, it is permissible if some of them intend their seventh for meat, and others intend their seventh for ’Aqiqah." And Allah the Almighty knows best.
What should one who doubts the validity of his ablution and performs it frequently do?
Whoever doubts the validity of his ablution after finishing it, his ablution is valid. This is because the default is the validity of the ablution, and because doubt after finishing an act of worship doesn`t affect its validity. And Allah the Almighty knows best.