I think I have solved the 'challenge'
You had hot link protection set on, which your site does not seem to like as it refused to download. I have put the need for a referrer On. But I will investigate a bit more as I was a little surprised.
There were also many 'permission' asset issues that needed sorting but these were not the real problem.
Also I suggest you may possibly need to sort out the Permissions settings for the Downloads. With the nice arrangement of user groups that you have I did not think you want everyone to be able to download everything. Also you have allowed many User Groups to create but not edit, which is unusual. You are of course protected as you have rightly limited access in many cases.
If you would like to suggest how you want which User Group to see what and which UG to be able to Download, Create, Edit from front end then I would be pleased to give some guidance, and set some up for you.
PS for testing purposes I did create a user in the Member UG but have deleted.