Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Is a menstruating woman obliged to pray during menses, and should she make up missed prayers?
All perfect praise be to Allah, The Lord of The Worlds A menstruating woman is prohibited from prayer during her menses, and she isn`t obliged to make up missed prayers. And Allah Knows Best.
Is my son who was breastfed one filling time by my aunt considered a brother to her children?
The baby who was suckled five sporadic times by a woman is considered a son/daughter of hers.
Is it permissible for me to name my daughter "Leen"?
“Leen” means “ease”, and there is no harm in giving your daughter that name.