Describe What A File Does

My site was hacked, one of the SQL tables was injected, and several MYSQL dumps were made and downloaded. The hacker appears to have done it with the attached file, which was uploaded to a directory with 777 permissions. I can pay $5 for it to be done. Can anyone tell me what the file allows the hacker to do (i.e. how was he able to inject into the database without credentials), and what I should check for other than looking at all modified files since the site was hacked, cleaning the database, and changing all directory permissions to 755? Also, how sophisticated was this hack? FILE HAS BEEN UPLOADED FOR YOUR REVIEW HERE: [login to view URL] WARNING: The file triggers my antivirus, although it is just a PHP file. View at your own risk, obviously. Besides describing what the file does, I need these questions answered: 1. Does that script allow the hacker to edit existing files 2. How does that script allow the hacker to access the mysql database without password/username 3. How does that script allow the hacker to download/edit the database without password/username 4. Is it a basic script anyone can get or a custom one