As a rule, you can’t use FTP to access the database. The database is at some level a series of files, but you never access it directly as such. MODx does supply a tool to dump the database as ganeshXL pointed out. You can also use other GUI tools such as
phpMyAdmin or the
mysqldump command line tool. I prefer the latter because it doesn’t suffer from the same memory restrictions that a web-based tool does.
The reason that many web apps include seemingly pointless
index.php files is not just to torque you off: sometimes webservers are configured to list directory contents if there isn’t a valid index file, e.g.
http://yoursite.com/some/folder/no/doc/specified/ (note the trailing slash identifies that as a folder). Most servers will serve the index file as the default page, but some of them will show the directory contents if they don’t have an index file (i.e. the server "indexes" the directory for you), and THAT can be a bad security breach. Make sense? It has nothing to do with your user role.
Lastly: UPGRADE THY VERSION.