Images Not Uploading to sites/default/files/*
Please check admin/config/media/file-system page on your site to see if the file directories are set correctly and accessible by Drupal. It's possible the server is configured differently from your local installation or the relative directories are set incorrectly in the configuration fields.

As for the comments about permissions and ownership - it seems you can run chmod on the directory, so the intention was that you would run chown on the directory to set the owner to the Apache group (on Ubuntu it www-data).