Hi,
sorry for late reply, was night for us

Is it possible to show the author and avatar in other components?

Yes, this is possible. Author plugin works only for Joomla articles, to enable avatar you can go to Extensions->Plugins and search by "Easy Profile - Author plugin", you will see a option to show avatar.
For other components there are differents ways to show Easy Profile avatar:
1) Component have a built-in integration with Easy Profile....of course this is the most simple case
2) Component have a built-in integration with Jomsocial. it is much older and more popular than Easy Profile, so there are many components that include an integration with it. We have developed a plugin that simulate the installation of Jomsocial but retrieve avatar and profile link from Easy Profile:
- Install jomsocial bridge, you can find it in our download area
- Configure your component to retrieve avatar and profile link from jomsocial
NOTE: jomsocial bridge does not works with all components. We have tested it only in a few components http://docs.easy-profile.com/index.php/article/jomsocial-bridge
3) you can customize the view of the component to retrieve avatar from Easy Profile for example with a code like this:

require_once(JPATH_SITE.'/components/com_jsn/helpers/helper.php');

$user=JsnHelper::getUser($user_id); // $user_id should be the id of the user

echo $user->getField('avatar');

Docs at http://docs.easy-profile.com/index.php/article/jsnuser-object

JsnUser Object, but did not find a solution there

Can you please post me your code, we will check if there is some error