Actually you need to modify a few files in order to achieve this, perhaps you can try following and see how it goes but do note our support scope is not cover customisation.
Friend request :
JoomlaFolder/administrator/components/com_easysocial/includes/friends/friends.php request method
It did pass in the request user id variable
requesterId
So you can use this requesterId variable in this email template file ->
JoomlaFolder/components/com_easysocial/themes/wireframe/emails/friends/request.php
For example :
// current user object
$user = ES::user($requesterId);
// get the address custom field data belong to this user id
// this 'ADDRESS' is your address custom field unique key , you can get it from backend > Easysocial > profile type > custom field > edit that address custom field > copy that unique key
// When you print out this $customField, you will get this address data
$customField = $user->getFieldValue('ADDRESS');
New registration :
JoomlaFolder/administrator/components/com_easysocial/models/registration.php notifyAdmins method
But this one by default it didn't pass in the user id, so you have to manually add this variable in this method, you can check my screenshot here :
http://take.ms/Bl4bw
Once you got this variable, you can use this variable
userId in this following email template file
JoomlaFolder/components/com_easysocial/themes/wireframe/emails/registration/moderator.approvals.php
JoomlaFolder/components/com_easysocial/themes/wireframe/emails/registration/moderator.login.php
JoomlaFolder/components/com_easysocial/themes/wireframe/emails/registration/moderator.verify.php
JoomlaFolder/components/com_easysocial/themes/wireframe/emails/registration/moderator.auto.php
For example :
// current user object
$user = ES::user($userid);
// get the address custom field data belong to this user id
// this 'ADDRESS' is your address custom field unique key , you can get it from backend > Easysocial > profile type > custom field > edit that address custom field > copy that unique key
// When you print out this $customField, you will get this address data
$customField = $user->getFieldValue('ADDRESS');
Hope this will help.