Adding a block with query in homepage

In both your queries you are doing it wrong. You are running a separate instance of WP_Query for every argument set

$args = array( 'posts_per_page' => $count, // Limit count ); 
$query = new WP_Query( 'cat=1' ); 
$query = new WP_Query( $args );

Should be

$args = array( 'posts_per_page' => $count, 'cat' => 1 );
$query = new WP_Query( $args );