What is true in the case of honey bees?

In Barr body (sex-chromatin) of a normal female:

Given below are two statements.
Statement $I$ - $X$ Chromosome has a large amount of euchromatin and a small amount of heterochromatin.
Statement $II$ - The homologous region of the $X$ Chromosome contains a smaller number of genes than the $Y$ Chromosome.
In the light of the above statements,select the correct option given below:

In which of the following is male heterogamety $NOT$ observed?

Sometimes $XX$ males and $XY$ females are produced due to:

If a character is always transmitted directly from a father to all his sons and from their sons to all their sons,then which chromosome carries the gene for the character?