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 function wpestate_ajax_show_login_form in ajax_functions.php at line 1108

the javascript is in ajaxcalls.js

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

For register we have this event
jQuery(‘#wp-submit-register’).click(function () {
wpestate_register();
});

Function wpestate_login() is in ajaxcalls.s at line 1220 while wpestate_register() is at line 1171

For register function wpestate_register we call the php function wpestate_ajax_register_form located in ajax_functions.php at line 422
For login function wpestate_register we call the php function wpestate_ajax_loginx_form located in ajax_functions.php at line 604

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.