not all categories being displayed

by

I played with your code a little bit on my local WordPress. I think this should solve your problems.

Arguments for your first get_categories call, should look like this:

$args=array(
    'hide_empty'=>false,
    'orderby' => 'slug',
    'order' => 'ASC',
    //'include' => '5, 6, 7, 8',   - you don't need to include anything
    //'exclude' => '3, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26',   - no need to exclude anything either
    'parent' => $menuCat
);

And for the second one:

$args=array(
    'hide_empty' => false,
    'orderby' => 'slug',
    'order' => 'ASC',
    'parent' => $category->term_id
);

It works correctly on my WP.

I also would recommend to use <h3> tags to display subcategories.