“Moving to .org” means “moving from WordPress.com blog provider to your own installation of WordPress which you can download from wordpress.org” – just to clear out your first point.
And than, after you export all data from your wordpress.com account, while importing them to your local install, you’re asked to automaticly download all images. Answer yes and your images get donwloaded from your previous account and uploaded to your new install.
About the thing with your hardcoded urls. I’m using this SQL script to programatically rewrite old URLs after moving to new domain:
UPDATE wp_options SET option_value = replace(option_value, 'http://wordpress.com', 'http://wordpress.org') WHERE option_name="home" OR option_name="siteurl";
UPDATE wp_posts SET guid = replace(guid, 'http://wordpress.com', 'http://wordpress.org');
UPDATE wp_posts SET post_content = replace(post_content, 'http://wordpress.com', 'http://wordpress.org');
UPDATE wp_postmeta SET meta_value = replace(meta_value, 'http://wordpress.com', 'http://wordpress.org');
Replace all http://wordpress.com by your formal URL and http://wordpress.org by your new domain (either example.com, example.org, example.cz – whatever) and run this SQL from phpmyadmin/adminer (or similar piece of software) of your new DB