CUSTOMER

Name, Surname, Firstname...

  $firstName = $customer->getFirstname();
  $lastName  = $customer->getLastname();
    $fullName  = $customer->getName();

Verify if there is someone logged in

 Mage::getSingleton('customer/session')->isLoggedIn();

Get Group ID of logged in Customer

 Mage::getSingleton('customer/session')->getCustomerGroupId();