Do not edit the Twenty Eleven theme. It is the default WordPress 3.2 theme and having access to an unedited version of the theme is vital when dealing with a range of site issues.
Create a child theme for your customisations. Once your child theme is active, start by sorting out the markup errors. Then move onto the CSS errors.
http://codex.wordpress.org/Validating_a_Website
If you continue to have problems with IE, consider conditional comment CSS