A plugin that retrieves the visitor's country information (using MaxMind's GeoIP local dat file)
No. It uses local database (dat file).
No. The accuracy of MaxMind's GeoLite City database is far from perfect; combined with a much bigger database, there's no much point supporting it in this plugin. Shall there be such a demand, a separate city plugin will be written.
Not at the moment, but this will be implemented shall there be a demand.
The plugin will go up in version periodically to reflect MaxMind's new database. You can always update it manually by downloading it from here, uncompress, and upload to the plugin directory.