Salman is Katrina's date.
As no two of them have the same number of preferred traits - from (1), exactly one of them has none of the preferred traits and exactly one of them has all the preferred traits.
From (4) and (5), there are only two possibilities:
* Shahrukh & Salman both are tall and Ajay & Akshay both are fair.
* Shahrukh & Salman both are short and Ajay & Akshay both are dark.
But from (2), second possibility is impossible. So the first one is the correct possibility i.e. Shahrukh & Salman both are tall and Ajay & Akshay both are fair.
Then from (3), Ajay is short and handsome.
Also, from (1) and (2), Shahrukh is tall and fair. Also, Akshay is the person without any preferred traits. Salman is Dark. Shahrukh and Salman are handsome. Thus, following are the individual preferred traits:
Salman - Tall, Dark and Handsome
Shahrukh - Tall and Handsome
Ajay - Handsome
Akshay - None :-(
Hence, Salman is Katrina's date.