How do I access the parameters fields of hook_mail_alter(&$message)?
The message entity is stored in $message['params']['contact_message'] and it contains all the values from the contact form. Given that it's an entity of type contact_message, you can operate with get() method to get the values of any field that your contact message might have. Example:

/**
 * Implements hook_mail_alter().
 */
function mymodule_mail_alter(&amp;$message) {
  if (isset($message['id']) &amp;&amp; $message['id'] == 'contact_page_mail') {
    /** @var \Drupal\contact\Entity\Message $contact_message */
    $contact_message = $message['params']['contact_message'];
    // Get sender's name.
    $sender_name = $contact_message-&gt;getSenderName();
    // Get sender's mail.
    $sender_mail = $contact_message-&gt;getSenderMail();
    // Get subject.
    $subject = $contact_message-&gt;getSubject();
    // Get message.
    $message_body = $contact_message-&gt;getMessage();
    // Get the value of "field_request" field.
    $request_value = $contact_message-&gt;get('field_request')-&gt;getValue();
  }
}