SQL is the language in which we speak to databases... Server Query Language. Each engine, such as Oracle, SQLite, Microsoft SQL, PosgreSQL and MySQL each have their own differing interpretations, but it's all (very roughly) the same. Because it's both powerful and free, Plogger relies on MySQL. You need a MySQL database set up on a server for Plogger to store all of your installation data. If you contact your hosting provider, they can likely help you out.
In regards to the latter problem, a good "chmod 755" on each of the above directories should do it. Most FTP programs allow for changing of permissions via FTP. I use FileZilla (freeware) and it allows me to change permissions. You're looking to allow global (server) read/write permissions on those directories.