In the Customizer code you need to do following change to work. You dont need ta_pluton_social_link[facebook]
like array in Control. Check following example and modify accordingly to other fields also.
$wp_customize->add_control('facebook', array(
'label' => __('Facebook URL', 'ta_pluton'),
'section' => 'ta_pluton_social_links',
'settings' => 'ta_pluton_social_link[facebook]',
));
To fetch URL you can use get_theme_mod
. Check example below. Following snippet demonstrates fetching Facebook URL.
$ta_pluton_social_link = get_theme_mod( 'ta_pluton_social_link' );
$facebook_url = $ta_pluton_social_link['facebook'];