1) It looks like you switched to the Twenty Twelve theme. The menu on the site currently isn't fixed. But the CSS that you wrote will work, as long as you've correctly identified the ID of the nav bar for the theme that you are using.
2) If you are making CSS changes, don't make them directly to the theme's files. If/when the theme gets updated because of feature enhancements, bug fixes, or security patches, then your changes will be lost. Instead, either create a child theme or use a CSS plugin like Jetpack or Custom CSS Manager. If you are just making CSS changes, then using a plugin is simplest.
3) I don't think any of the Twenty X themes (Twenty Eleven, Twenty Twelve, etc), natively support a logo. You would have to create a child theme and edit a copy of header.php. Twenty Twelve & Thirteen allow you to have a header image, but it's not really the same as a logo. If you want to have a logo, I would suggest searching through the WordPress theme repository for a theme which supports a logo.