Should the Zakah (obligatory charity) giver tell the poor recipient that this is the Zakah of his money?
No, he shouldn`t. But, the Zakah giver should make an intention in his heart that it is the Zakah of his money when paying it to the poor. 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
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
A man who was on travel prayed Duhr as four Rakhas upon leaving Tafilah heading to Amman. However, on his way to Amman, he prayed Asir as two Rakhas (Shortened). Is what he did correct from an Islamic perspective?
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.
What he did is correct; he is liable for nothing before Allah The Almighty, since combining and shortening prayers during travel are two separate concessions. Therefore, it is permissible for a traveler to shorten prayer without combining it with another. And Allah The Almighty Knows Best.