Positioning problems IE vs Firefox

https://ceciliabjerling.com/wordpress/

I’ve positioned my search and login forms nicely in Firefox, but as always IE majorly screws it up. Could someone please take a quick look at my source code and see what I could change to make this compatible with both browsers. I didn’t make it anymore complicated than float left and right and margins. It also somehow messes up my right column, as you can see comparing the site in the two browsers. Thank you very much for any help with this! I’m obviously new to CSS which makes this all the more frustrating.