Can Dropfiles or some other combinations of components satisfy the following needs:

Hi,

Thanks for contacting us here about this extension.

- Must have the ability to upload large files up to 2 GB
- Must show progress of file uploading and confirm success/failure (and the mail confirmation must be sent to admin and user automatically)
- Must have folder hierarchy

These features are possible in our Dropfiles. For the folder tree you can go here:
https://www.joomunited.com/joomla-documentation/dropfiles/278-dropfiles-common-use#toc-2-manage-file-categories

- Must have "admin" and "user" privilege settings:
- "User" must only be able to view/upload/download/delete own files
- "Admin" must be able to upload files that can only be viewed by designated users

You can set the role for users to manage their files but the admin will have full access at backend.
That means admin can see and manage all files and categories in the dashboard.

- Must be secure as some files may be may have patents or Intellectual property associated to them

Yes, all files uploaded to Dropfiles are secured certainly.

Hope it helps!
Kind regards,