First of all, I need to clear myself that I am not look at Deb's NSGAII C implementation. I am trying to answer your question from algorithmic point of view. 

1. Why is it necessary to sort initial population? Because from initial population, the algorithm will produce offsprings. For that the algorithm require selection operator, and for selection, the only requirement is dominance comparison. Therefore, the initial population is required to evaluate not sorting.

2. In selection process, no crowding distance is used. Selection process only consideres constraint violation and dominance relation.

Cheers. 

@Md. Shahriar Mahbub, Thanks for your answer.

1. In selection process, crowded-comparison operator (need non-domination rank and crowding distance value) is used, doesn't it? so crowding distance is used. What did you mean "dominance comparison", if it implemented in pseudocode? It is like:

A style:

     if(p dominate q) then

          select p

     endif

     if(q dominate p) then

          select q

     endif

or is like:

B style

     if(p_rank < q_rank) then

          select p

     endif

     if(q_rank < p_rank) then

          select q

     endif

Use A style or B style?

Then which one should be selected if p and q not dominate each other ("dominance comparison" = style A) or p rank = q rank ("dominance comparison" = style B)?

Hi, 

The original version of binary tournament selection is similar to your style A. If p and q do not dominate each other and one can selected randomly.

One more thing, the original version of binary tournament do not use ranking or crowding distances.

The goal of fast non-dominated sorting is to place individual into fronts right? If selection process use style A (dominance comparison) not ranking (front) comparison, it mean that initial population does not need to be sorted using fast non-dominated sorting?

yes,  it does not require.