The login and register functions are made via ajax. Meaning : a event is triggered in javascript , and inside this function event a register/login php function is called. This function will return the result back to the javascript ,where we will redirect the user to his profile page or we will display other relevant information.

For pop window login and register functions

-> the html code is in function wpestate_ajax_show_login_form in wp-content\themes\wprentals\libs\ajax_functions.php file

-> the javascript is in wp-content\themes\wprentals\js\ajaxcalls.js

For login we create this event
jQuery('#wp-login-but').click(function () {

For register we have this event

jQuery('#wp-submit-register').click(function () {

Function wpestate_login()  and function wpestate_register() are in wp-content\themes\wprentals\js\ajaxcalls.js .

For register function wpestate_register we call the php function wpestate_ajax_register_form located in wp-content\themes\wprentals\libs\ajax_functions.php .
For login function wpestate_register we call the php function wpestate_ajax_loginx_form located in wp-content\themes\wprentals\libs\ajax_functions.php .

The above php function will handle the register/login actions and return the result to the javascript function. In there on the succes branch of the ajax call we will execute actions corresponding with the success or failure of login and register process.