How show categories in admin and get that selected to show posts in index

You can use Advanced Custom Fields to add two fields where the admin can select a category. On your index page, you then check the two fields using get_field for which category you want to display.

The field can return a WP taxonomy object, or just the category ID (which I have used). In your index, you can then get the posts:

$category_id_1 = get_field('category_1'));
$category_id_2 = get_field('category_2'));

$container_1_posts = get_posts(array(
   'posts_per_page'   => 5,
   'cat'              => $category_id_1,
   'orderby'          => 'date',
   'order'            => 'DESC',
   'post_type'        => 'post',
   'post_status'      => 'publish',
)); 

$container_2_posts = get_posts(array(
   'posts_per_page'   => 5,
   'cat'              => $category_id_2,
   'orderby'          => 'date',
   'order'            => 'DESC',
   'post_type'        => 'post',
   'post_status'      => 'publish',
));