How to theme file display?

I'm looking for some pointers. I want to do 2 things:

Please only ask one question per issue. Since "How to theme file display?" is the subject I'll answer that question.

About the second question, I think I can use "theme_filefield_file()", correct?

Yep, copy to your template.php, rename to [name_of_your_theme]_filefield_file(), and change as necessary.

Also, it seems that I can't write a template file for a specific filefield, but only for filefields in general. Is that correct?

There's only one theme function available per formatter (like the theme_filefield_formatter_default() function), but you can check which field the file came from by checking $element['#field_name'].

Note the "theme_filefield_formatter_default()" theme function is only used for the "Generic files" display formatter.

function [theme_name]_filefield_formatter_default($element) {
  $file = $element['#item'];
  $field = content_fields($element['#field_name']);

  if ($field['field_name'] == 'field_image') {
    $output = 'Special output just for the field_image field';
  }

  $output .= theme('filefield_item', $file, $field);
  return $output;
}

Is it possible to add an own field formatter?

Yes, make your own module and implement hook_field_formatter_info(). In truth many other modules already extend FileField's formatters to provide image display, audio or video players, thumbnails, etc. You can look at the filefield_field_formatter_info(), imagefield_field_formatter_info(), or imagecache_field_formatter_info() for some examples of this.

advseb wrote up a handbook page at http://drupal.org/node/420570