Can I create two sites with a single user login?
The mechanism which you are talking about called SSO (Single Sign On). There are modules in Drupal to achieve SSO but it would depend upon your site setup like whether 2nd site is sub-domain of the first or both are sub-domain of some other etc..

In case one of them second level domain then you can use Bakery. I have used it successfully.

I have heard so much about CAS module too though never used it. You can go through the documentation of the module and find out whether it fulfil your need or not.

You can have a look here on comparison between all SSO modules available in Drupal.

Regarding auto update, I am not sure it can be done easily with any of them. You will have to write your own code maybe.