Is it permissible for one to give the Zakah (obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his indebted , or poor brother.
What is the ruling on working for orphans' institution?
Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There is no sin in working for orphans` institution. And Allah The Almighty Knows Best.
Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
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 as 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