How to make user pictures public files? I need to pass some URLs to user pictures via AJAX. I can't, however, pass private://filename.jpg because client can't open it.
Are there some settings to configure where I can change to public space?
You need to change the image field associated with the user profile to Public, and then you need to migrate any existing private image files to the new public directory.  Here's a write-up on working with files in Drupal 7.