Actually, I might lean more towards IE's interpretation here. And that is after trying so hard not to leave your site as soon as it yelled at me in two consecutive pop up alerts.
Your buttons are covered up by your main area because your main area has negative margin which pushes it higher up and hides the buttons. Given that (no specific z-index set) lower elements (in the code) have higher z-index than higher, your main area is covering the buttons.
As for the border around it. If you do not specify it, how should the browser know what you want. Apparently they both fall back to their default and you clearly like the FF effect but not IE effect. I guess you should override it with your style.