Can Civiccrm do this?
Welcome to CiviCRM 

CiviCRM can do all the above listed features and more 

But first you need know more about wordpress and CiviCRM - you can do this by palying around in Civicrm wordpress demo site which will give you more idea regarding your need 

Demo Link: https://civicrm.org/sandboxes - 
http://wpmaster.demo.civicrm.org/wp-login.php

refer: https://civicrm.org/will-civicrm-meet-your-needs

All the best for your CiviCRM Learning 

I guess this helps !!!