Is it permissible for me to name my daughter "Leen"?
“Leen” means “ease”, and there is no harm in giving your daughter that name.
Is it permissible for a Muslim woman to leave her house adorned and without wearing her proper Islamic attire?
A Muslim woman isn't permitted to leave her house adorned and without wearing proper Islamic attire. And Allah Knows Best.
What is the ruling on working for a company that manufactures cigarettes?
All Perfect Praise is due to Allah, The Lord of The Worlds
Working for a company that manufactures cigarettes is forbidden because smoking itself is forbidden, so its production, selling and circulation are forbidden as a result since they aid in committing sin, and whoever aids in that is like the sinner himself. And Allah Knows Best.
What is the ruling on a person who broke the fast a day in Ramadan due to hardship?
He/she is obliged to make up that day.