How to print redirected query string variables to the page?

First, year is already a WordPress query var used for date-based archives, you should change that to something unique to prevent possible conflicts.

To use your own query vars within rewrite rules, you need to add them to the list of known vars:

function wpd_query_vars( $qvars ) {
  $qvars[] = 'my_year';
  $qvars[] = 'make';
  $qvars[] = 'model';
  return $qvars;
}
add_filter( 'query_vars', 'wpd_query_vars' , 10, 1 );

Then you can output their values in the template with get_query_var:

echo get_query_var( 'model' );