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Hello Genesis !
The mentioned functions have the following analogs in UNA:
1) isLogged (inc/profiles.inc.php)
2-3) BxDolAccount::getInstance()->getDisplayName and BxDolAccount::getInstance()->getDisplayEmail (inc/classes/BxDolAccount.php)
4) no analog :-( you need to call the MySQL query from the BxDolDb->getRow() method.