PHP variables are not evaluated inside of single quotes, only double quotes, therefore change the following:
$subject = 'Inquiry from $name';
//to
$subject = "Inquiry from $name";
Also for the email portion, you're not doing anything with it... so do something with it.
$message = $comments1 . "\n\n" . $comments2 . "\n\n" . $email;
Now it sends the email as well.