Is there a Webfm Database API?

Mario,
thank you for asking and helping to make webfm better. I'll give it a shot, but I think you might find some more answers by looking through the issue queue.

What is the procedure to call an API of WebFM module from another module in drupal?

There no actual API - there are no hook or something that is called. You might rather want to call webfm_insert_file - it gives you a TRUE/FALSE return value and thus might be nicer.

I could imagine a scenario like this: You write a custom module that uses a kind of hook that your filebrowser provides. This hook triggers webfm_insert_file and your done :-)

Which is the precise API (I mean the upper layer) to call to force webfm_dbinsert_file?

As I said for a single file I'd rather use webfm_insert_file(). You probably noticed the usage:

/**
 * webfm_insert_file - inserts a file into the webfm_file table
 *
 * @param string  $path - path relative to drupal root
 * @param string &$err_arr - ref to error array for client feedback
 *
 * @return bool - TRUE if query executed successfully, otherwise FALSE
 */

Well, I hope this helps a little bit,
Happy Holidays.

$relative_filepath = 'bla';
$errors=array()

 module_load_include('module','webfm');
webfm_insert_file($relative_filepath,$errors);