echo $category[0]-> cat_name; shows only one category name

In your code:

$category = get_the_category(); echo $category[0]-> cat_name;

get_the_category() returns and array of WP_Term objects. You are getting the first one from the array, and echoing only that one category name.

I'd recommend using get_the_category_list() instead.

$categories_list = get_the_category_list( esc_html__( ', ', 'html5blank' ) );
if ( $categories_list ) {
    echo '<li><p class="meta-txt">', esc_html__( 'Category', 'html5blank' ), '</p><p class="meta-des">', $categories_list, '</p></li>';
}

There is also the method get_the_tag_list() which you can use in a similar fashion to get the tags as you mentioned wanting to do that.

Altogether you would end up with something similar to this:

     <div class="row">
        <div class="col-lg-12 post_meta">
          <ul>
            <?php
            $categories_list = get_the_category_list( esc_html__( ', ', 'html5blank' ) );
            if ( $categories_list ) {
                echo '<li><p class="meta-txt">', esc_html__( 'Category', 'html5blank' ), '</p><p class="meta-des">', $categories_list, '</p></li>';
            }
            $tags_list = get_the_tag_list( '', esc_html_x( ', ', 'list item separator', 'html5blank' ) );
            if ( $tags_list ) {
                echo '<li><p class="meta-txt">', esc_html__( 'Tag', 'html5blank' ), '</p><p class="meta-des">', $tags_list, '</p></li>';
            }
            ?>
            <li>
              <p class="meta-txt">Published</p>
              <p class="meta-des"><?php the_time('F j, Y'); ?> </p></li>
            <li>
              <p class="meta-txt"><?php echo get_comments_number(); ?> Comments</p>
              <p class="meta-des"><?php if (comments_open( get_the_ID() ) ) comments_popup_link( __( 'Leave your thoughts', 'html5blank' ), __( '1 Comment', 'html5blank' ), __( '% Comments', 'html5blank' )); ?></p></li>
          </ul>
        </div>
      </div>