Only download manager we provide is CB Package Builder. It's primarily meant for packaging Joomla extensions for installing multiple things at once, but it supports custom package types that download normally (e.g. see our documentation downloads for example). See the below product page for more details.

www.joomlapolis.com/addons/cb-package-builder

It does not have statistics or notifications. Notifications I suppose you could do via CB Auto Actions acting on package create trigger, but that only fires when a new package is created. As for fields normal CB can already provide custom field functionality.

Our downloads page below is powered by CB Package Builder as well.

www.joomlapolis.com/downloads

You can also give it a try on our demo site below.

demo.cbdemosites.com/