How do I get the Unix timestamp? I want to use format_date(), but it requires a Unix timestamp and my dates are ISO.  

Is there a drupal way to convert ISO date to Unix timestamp? If I use strtotime, I lose my timezone offset.
You shouldn't use format_date() anymore.  You should create a DrupalDateTime object, and then use the format() method.

$date = \Drupal\Core\Datetime\DrupalDateTime::createFromFormat('c', $my_iso_8601_date);
$my_rfc2822_string = $date-&gt;format('r');