The data is not stored in the session but in the database.
You can see it in the table hikashop_address
It's not possible to edit your email address via HikaShop. Joomla might allow that (I don't think it does) if you're using a normal user account.
I'm not sure which mode you're using but if you're in "no registration" mode, you can use the code:
$app = JFactory::getApplication();
$app->setUserState( HIKASHOP_COMPONENT.'.user_id', 0);
To force the unset of the user data.
And thus you would see the user information field again once that code is run.
If you want to make it a button, that's possible by adding the HTML of your button in one of the view files of the view "checkout" via Display>Views which would redirect to the checkout with an additional parameter that you would then check to run that code and the do a redirect:
blog.calebnance.com/joomla-1.5/code/how-...5-mvc-component.html