The login and register functions are made via Ajax. This means an event is triggered in JavaScript, and a register/login PHP function is called inside this function event. This function will return the result 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 for register is in function wpestate_register_form_function in wprentals-core\shortcodes\shortcodes.php

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

The PHP code for processing the registration is located in the function wpestate_ajax_register_form in libs\ajax_functions.php

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

To register we have this event

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

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.