One (?) step ahead...
In author-template.php i found at line 84 the following:
function the_author_link() {
if (get_the_author_url()) {
echo '<a href="' . get_the_author_url() ...
That means to me something like somebody undesigned inserted get_the_author_url() in here. No wonder that the_author_link echoes the authors home-url. This substitution disables the native sense of this function and just doubles get_the_author_url()!
After wondering a while about this i found in line 138:
/* the_author_posts_link() requires no get_, use get_author_posts_url() */
function the_author_posts_link($deprecated = '') {
global $authordata; ....
Unfortunately i have not enough time to check this out in older versions of WP. But setting a variable $deprecated, that never is used within this function - as well as in many others - is looking to me at least a little bit strange.
Next: I really couldn't figure out, why the returned ancortext of the_author_posts_link did not match with the url of my author-page. The echoed link was always /author/admin/ instead of /author/myNickname/.
What means, that the database-values of my nickname / nicename were unchangeble by changing settings in the adminpanel. Updating the permalink-structure in admin-panel made no changes too. I succeeded with this after changing my user_nicename in the wp_users table manually with phpMyAdmin.
Now using the_author_posts_link() anything runs perfect - with other users too.
Thanks to Mr. and Mrs. Strange, this has been a nice evening.
Cheers from Bavaria