Add feature to display who downloaded the files by user and ip?

It possible but this will creates a possibly huge database table since thousands of users may download thousands of files every day.

That's the reason we did not implement this feature.
We need to put some limitation to avoid the download record size become huge. For example, download records are kept only for a certain short period of time and older records are deleted automatically.

I can taylor it and create a custom version for a specific sites that has this feature. BTW, Drupal 7 version has some additional features such as "remove duplicate download within a same day from the same IP address"...

I will counter-port such features back to D6 version later.

yes, I need too to check user's downloads with drupal 6, thanks!
I?m not expert about it, but why this module can track users and you can't all? http://drupal.org/project/private_download