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.
What are the pillars of fasting?
The pillars of fasting are intention and abstaining from all nullifiers of fasting from dawn to sunset.
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.
What is the ruling on eating and drinking at night after making the intention? Is it necessary to renew the intention?
Eating and drinking at night, even after making the intention (for the next day), does not affect the fast, and it is not necessary to renew the intention after eating and drinking.