Knowing installed Joomla version

That is explicitly available in the Joomla file:

Joomla Root Directory\libraries\joomla\version.php


var $PRODUCT = 'Joomla!';
var $RELEASE = '1.5';
var $DEV_STATUS
var $DEV_LEVEL
var $BUILD
var $CODENAME
 var $RELDATE
var $RELTIME