Why all posts are getting Justify after publishing?

What’s the original form?
Link to your site?
Anyway try adding this to your custom css:

.entry-summary {
    text-align: initial;
}

Hi, yes use the css above

I don’t get the “gap” issue, sorry, can you make a screenshot with a huge arrow pointing to the issue? 😀

About the caption, unfortunately is a bug fixed in the latest version 3.3.9

can you update your theme and confirm it?

What about moving the tagline below the logo+navbar?
To do this you need a child-theme and add this to your child-theme functions.php:

add_action('wp_head', 'some_tagline_stuff');
function some_tagline_stuff(){
  if ( ! class_exists('TC_header_main') && method_exists('TC_header_main', 'tc_tagline_display') )
    return;

  remove_action( '__navbar', array(TC_header_main::$instance, 'tc_tagline_display') , 20);
  add_action('__header', 'display_tagline_below', 40);
    function display_tagline_below(){
      $html = sprintf('<div class="container below"><%1$s class="site-description">%2$s</%1$s></div>',
        apply_filters( 'tc_tagline_tag', 'h2' ),
        apply_filters( 'tc_tagline_text', __( esc_attr( get_bloginfo( 'description' ) ) ) )
        );
      echo apply_filters( 'tc_tagline_display', $html );
    }
}

then add this to your child-theme style.css:

@media (max-width: 979px){ .container.below {display:none;} }

About the menu on one line, it depends on the space between the elements, you have to play with the padding, and font size:
So, something like:

.navbar .nav>li>a {
    padding-left: 10px;
    padding-right: 10px;
    font-size: 14px;
}

But you might need adjustments for different viewports, see media queries.