Magento – How to add new field in billing address in magento 2 and how to save that attribute data

for getting data change

from

$customer = Mage::getModel('customer/customer')
        ->load($customerId)->getData(); // insert customer ID
    //Mage::getModel('customer/customer')->load($id)->getData();

    foreach ($customer->getPrimaryBillingAddress() as $address)
    {
        $data = $address->toArray();
        var_dump($data);
    }

to

   $customer = Mage::getModel('customer/customer')
        ->load($customerId); // insert customer ID
    //Mage::getModel('customer/customer')->load($id)->getData();
    echo "<pre>";
    print_r( $customer->getPrimaryBillingAddress()->getData());

If you want to update primary billing address telephone from mobile number(custom attribute) IF telephone field is empty

then using customer address model(Mage::getModel('customer/address')) update this address telephone.

$address=Mage::getModel('customer/address')->load($customer->getPrimaryBillingAddress()->getEntityId());
$address->setTelephone($customer->getMobile());
$address->save();

I think below link will be help to you. http://devdocs.magento.com/guides/v2.0/howdoi/checkout/checkout_edit_form.html