1. soru ilgili tema elimde olmadıgı icin malesef net yerini söyleyemiyorum ancak profil sayfasının kodlarından temizlene bilir
2 ci soru ise aşağıdaki kodu function .php dosyanıza ekleyin

add_action( 'register_form', 'myplugin_register_form' );
function myplugin_register_form() {

$first_name = ( ! empty( $_POST['first_name'] ) ) ? trim( $_POST['first_name'] ) : '';
$last_name = ( ! empty( $_POST['last_name'] ) ) ? trim( $_POST['last_name'] ) : '';

?>
<p>
<label for="first_name"><?php _e( 'First Name', 'mydomain' ) ?><br />
<input type="text" name="first_name" id="first_name" class="input" value="<?php echo esc_attr( wp_unslash( $first_name ) ); ?>" size="25" /></label>
</p>

<p>
<label for="last_name"><?php _e( 'Last Name', 'mydomain' ) ?><br />
<input type="text" name="last_name" id="last_name" class="input" value="<?php echo esc_attr( wp_unslash( $last_name ) ); ?>" size="25" /></label>
</p>

<?php
}

//2. Add validation. In this case, we make sure first_name is required.
add_filter( 'registration_errors', 'myplugin_registration_errors', 10, 3 );
function myplugin_registration_errors( $errors, $sanitized_user_login, $user_email ) {

if ( empty( $_POST['first_name'] ) || ! empty( $_POST['first_name'] ) && trim( $_POST['first_name'] ) == '' ) {
$errors->add( 'first_name_error', __( '<strong>ERROR</strong>: You must include a first name.', 'mydomain' ) );
}
if ( empty( $_POST['last_name'] ) || ! empty( $_POST['last_name'] ) && trim( $_POST['first_name'] ) == '' ) {
$errors->add( 'last_name_error', __( '<strong>ERROR</strong>: You must include a first name.', 'mydomain' ) );
}
return $errors;
}

//3. Finally, save our extra registration user meta.
add_action( 'user_register', 'myplugin_user_register' );
function myplugin_user_register( $user_id ) {
if ( ! empty( $_POST['first_name'] ) ) {
update_user_meta( $user_id, 'first_name', trim( $_POST['first_name'] ) );
update_user_meta( $user_id, 'last_name', trim( $_POST['last_name'] ) );
}
}

kaynak : https://codex.wordpress.org/Customiz...istration_Form

yada eklenti olarak da yapabilirsiniz
https://wordpress.org/plugins/user-registration/