Fuji has been tested on IE7 for compatibility issues, yet there may always be something that was left out. From the practical perspective, this version of Explorer is used by less than 1% (and falling) of the Internet user community, and is officially not supported by large websites such as e.g. Youtube. I will do my best to help in this situation – please provide a link to your website so that I could have a look at the code and the issues you’ve described.
I’ve worked out the fixes for the secondary menu submenu and recent posts slider in IE7. Please download this file from my repository, unzip it, and upload into the theme folder (/wp-content/themes/Fuji/), replacing the existing file if it exists.