You won't use rdp to communicate with windows.
You can use winrm, 3389 is the port.
windows_upadate module is available in ansible.
You can use * in category name Or you can create an array and pass the update type.
Reboot too can be achieved by giving a boolean attribute.
Rather taking system update in the same play, use another play for ping test and system info so that you will get a comprehensive list.