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 me to make up for my late father`s missed fasts? and should I make an intention to this end by saying: "I intend to make up for my late father`s missed fasts?
It is permissible to fast on behalf of the deceased father in order to make up for his missed fasts, and you should make the intention for offering fast from night time, but uttering the intention isn`t a condition. And Allah Knows Best.
Is it permissible for the man to go out wearing shorts?
All Perfect Praise is due to Allah, The Lord of The Worlds
It is permissible so long as his Awrah (private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed. And Allah Knows Best
Should one obey his mother even if she was wrong?
Obeying one`s mother is an obligation in matters that are beneficial to her and so long as she didn't drive her children to commit an act of sin.