Can you insert the following code into css/ie8.css and see if some of these issues resolve. My mistake – I have this incorporated into the theme for quite sometime now but it slipped from the HTML version.
/* Do not allow IE to respond to browser resizes */
#sticky-menu-area, #mobile-menu .inner, #header-area, #custom-before-content-area, #before-content-area, #bottom-area,
#footer, #main { min-width: 1140px; }
body.fluid-width-page .segment-content, body.fluid-width-page .breadcrumbs {
min-width: 1140px;
}
This is essential for IE8 since IE8 does not support media queries and we should not be decreasing the content width with resize of browser window.
For the navigation issue you mention, I am still not able to understand the problem. Here is the screenshot that I was able to get from the site with the dropdown working fine on resizing and it is restored back to original function on increasing the browser size without issues.
I want to mention that sticky menu will disappear when you resize the browser to a certain width (767px viewport) and start to scroll up or down. On small sized tablets and smartphones, you will not see the sticky menu due to space constraints. I appreciate you taking the pain to report these issues with the screenshots but the navigation menu issue is still not clear to me 🙁