@emilottersten What you’ve got setup is something completely custom, it looks like, in regards to the slider. I believe the issues you’re having in IE have something to do with how you have the slider positioned in your header in your custom.css.
I’m thinking it has something to do with how you’ve floated the entire slider. You could possibly set the header up with two DIV’s floated next to each other, but that both have a width of 50%. Then, put your slider inside of that second 50% DIV. But I think the main point is that by trying to float the slider you’re messing with how Flexslider is trying to determine the width and rotate through the slides. The slider needs to be sitting normally as a non-floated block-level element in a container with a structured width.