Inside observer,
$order = $observer->getEvent()->getOrder();
$orderFromFront = $order->getRemoteIp();
$guestCustomer = $order->getCustomerIsGuest();
groupId = $order->getCustomerGroupId();
$firstname = $order->getCustomerFirstname();
$lastname = $order->getCustomerMiddlename();
$lastname = $order->getCustomerLastname();
$prefix = $order->getCustomerPrefix();
$suffix = $order->getCustomerSuffix();
$dob = $order->getCustomerDob();
$taxvat = $order->getCustomerTaxvat();
$gender = $order->getCustomerGender();
$order = $observer->getEvent()->getOrder();
$orderFromFront = $order->getRemoteIp();
$guestCustomer = $order->getCustomerIsGuest();
$groupId = $order->getCustomerGroupId();
$firstname = $order->getCustomerFirstname();
$lastname = $order->getCustomerMiddlename();
$lastname = $order->getCustomerLastname();
$prefix = $order->getCustomerPrefix();
$suffix = $order->getCustomerSuffix();
$dob = $order->getCustomerDob();
$taxvat = $order->getCustomerTaxvat();
$gender = $order->getCustomerGender();
For shipping address,
$order->getShippingAddress()->getData()
And for billing,
$order->getBillingAddress()->getData()
You can get all type of customer data using observer.