Modifications on this site?
 

What mods are used on this forum, specifically the download mod that restricts certain users to be able to download files and the general format of the download section of this forum?

the modifications section of this site is a custom script for vBulletin.org and is not available for download.

Download restrictions are simply usergroup permissions.

Extending on this, although iirc this is not exactly how it's done here;

A simple way to do this is to create a new usergroup with custom permissions to download attachments from certain forums. All other usergroups (aside from admin/moderators) would have their permissions set to not allow downloading attachments from said forums.

Once that is in place you'll have to write a script that will move users between these usergroups depending on your custom restrictions. An easy way to do this would be setting up a vBcron task with your custom script and letting it run once every 30 minutes.

As for the 'database' look here at vB.org that is also an easy thing to do. First thing you do is make an array full of all the forumids from the forums that make up your file database. Use that array in a hook in the file index.php to exclude these forums from your main forum list.

Next create a new .php file and query the database for your file database forums with the same array. You can wrap the results in custom templates if you want or add some permissions code.

If you know what you're doing you can probably nock it out in a couple of hours.

And if you don't know what your doing you can do what most other sites do and use Geek Article Review System (GARS) and install the release module.