Google Drive anonymous download

Yes and no. For basic users, no you cannot see who accessed data on your Google Drive account. But if you upgrade to a Google Apps Unlimited or Google Apps for Education account you will have access to the Drive audit log. As explained here:

The Drive audit log lists every time your domain's users view, create, preview, print, update, delete, download, or share Drive content. This includes content you create in Google Docs, Sheets, Slides, and other Google Apps, as well as content created elsewhere that you upload to Drive, such as PDFs and Word files.

To access the Drive audit log, sign in to your Admin console and click Reports > Audit > Drive. The page displays the following information:

• Event DescriptionA summary of the event, such as "Larry created an item."
• UserThe user who performed the activity.
• DateThe date the event occurred (displayed in your domain's default timezone).
• Event NameThe action the user performed, such as View, Create, or Edit.
• IP AddressThe IP address from where the user performed the activity.
• File TypeThe type of Drive file the activity involves. OwnerThe user who owns the file.