Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Should a woman who broke her fast because of delivery make up for missed fasting days before the next Ramadhaan, and what is the expiation due on her in case she delayed making up for them ?
She should make up for missed fasting days before the start of next Ramadan if possible, but if she didn`t while being able to, then she is obliged to make up for them along with feeding a needy person for each delayed day of the missed fasting days. However, if she wasn`t able to make up for the missed fasting days before the start of next Ramadan, she has to fast a day for every day that she missed, and no ransom is due on her. And Allah Knows Best.
How long is the` Iddah (waiting period) of a divorced woman?
The waiting period (iddah) of a divorced woman who is pregnant is until she gives birth. If she is of menstruating age, her waiting period is three menstrual cycles. If she does not menstruate, her waiting period is three months. And Allah Knows Best.
Is it permissible to give Zakah (obligatory charity) to one`s poor sister, or brother?
It is permissible for one to give the Zakah to his poor sister, or brother if providing for them isn`t due on him, and the sister doesn`t receive sufficient provision from whomever that is due on. And Allah Knows Best.