No. To the best of my knowledge there is no relation between your XF avatar and your facebook one presently. The only benefit I am aware from the association process is when you are logged into facebook you will be automatically logged into any XF sites you visit, and can then perform social sharing such as likes, etc.
definitely needed, as my users coming from FB still show their default blank FB-avatar at my Forum (blue / white man).
Can this user (who is coming from FB) just change his avatar at my Forum, just as any other user can ?
Does a user who signed-up via FB need to associate his Forum-account with his user-account at Facebook? Why?
The reasons for associating a Facebook account with your XF account is to allow the automated login feature to work, and Likes to post on the user's account.
There is no means to link a user's fb avatar presently available.
If you use XenPorta and have the fb block on your portal page, then you will see user's fb's avatar appear there at random.
The only supported avatar linking within XF is Gravatar. If you encourage your user's to join that service, then they will gain the benefit on your site and any other forums they may join. That is why the service exists.