For 1st question
$args = array(
'post_type' => 'us_visa',
'posts_per_page' => -1,
'orderby' => 'post_date',
'order' => 'DESC',
'meta_query' => array(
array(
'key' => '_Passport',
'value' => $passport_num,
)
)
);
$query = new WP_Query( $args );
See Custom Field Parameters of WP_Query on Codex
For 2nd question, inside the loop use
<?php the_terms( get_the_ID(), 'visa_processing', '<p>', "https://wordpress.stackexchange.com/", '</p>') ?>
See the_terms docs on Codex
Sorry, I don’t understand the 3rd Question.