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
Is Zakah (obligatory charity) due on leased property, and how is it calculated?
Zakah isn`t due on the leased property itself, but on the saved income from that property if it reached Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over saving it.
Is it permissible for the mother to give her children from the Zakah (obligatory charity) of her money?
It is permissible for the mother to give her children from the Zakah of her money if they are Zakah-eligible recipients, and she isn`t obliged to provide for them.
Is it permissible for the woman who is observing Iddah after her husband`s death to sit with her daughter`s suitor, although their marriage contract hasn`t been concluded yet?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
A suitor who hasn`t concluded the marriage contract isn`t a Mahram*, so he must be treated as such. And Allah The Almighty Knows Best.
* The period a woman must observe after the death of her husband or after a divorce, during which she may not marry another man.
* In Islam, a mahram is a member of one's family with whom marriage would be considered haram, concealment purdah, or concealment of the body with hijab, is not obligatory; and with whom, if he is an adult male, she may be escorted during a journey, although an escort may not be obligatory.