WP-DownloadManager – Query most download per week/month etc

Simple answer: No.

Complex answer: After looking at the plugin’s source code, the downloads table used to store the stats is not structured such that you could just edit this single query to give you that kind of information. It would take a much more extensive rewrite of the plugin to handle your request.

Possible Workaround: The plugin has a function called get_recent_downloads which looks like it outputs a list of the newest files.