JQuery conflict

It is wrong for a plugin to use a different version of jQuery, so that every other plugin or theme that correctly uses WordPress’ jQuery version will have to be changed.

You’re looking at this the wrong way. The plugin is the one with the issue.

I’ve flagged to Developers.

Cannot reproduce the issue.
There must be some weirdness in your db option row.
You can, anyway, force those settings via code adding the following to your child-theme functions.php:

add_filter('tc_opt_tc_fancybox', '__return_false');
add_filter('tc_opt_tc_gallery_fancybox', '__return_false');

(always assuming you don’t have old core php files copied in your child-theme, like e.g. inc/class-fire-resources.php):

or:

//dequeue the fb script
add_action('wp_print_scripts', 'dequeue_fancybox_script');
//dequeue the fb style
add_action('wp_print_styles', 'dequeue_fancybox_style');
//force fancybox state js param to false
add_filter('tc_customizr_script_params', 'force_js_fancybox_to_false');
function dequeue_fancybox_script(){
  wp_dequeue_script('tc-fancybox');
}
function dequeue_fancybox_style(){
  wp_dequeue_style('fancyboxcss');
}
function force_js_fancybox_to_false( $params ) {
  if ( array_key_exists('FancyBoxState', $params ) )
    $params['FancyBoxState'] = 0;
  return $params;
}

Hope this helps