You're using the wrong type of quotes. In PHP, escape sequences aren't processed in single quotes, only in double quotes. So it should be:
$errorMessage = 'Some fields are empty!' . "\n"
. '$name= ' . $name . "\n"
. '$schedule= ' . $schedule . "\n"
. '$free_connection= ' . $free_connection . "\n"
. '$free_coffee= ' . $free_coffee . "\n"
. '$rating= ' . $rating . "\n"
. '$lat= ' . $lat . "\n"
. '$lng= ' . $lng . "\n";
echo $errorMessage;