Hi Barry,
I'm Business Branding's developer. I'm not sure what is causing the issue with everything squishing to the right. It may be the background image with your telephone number and email. If you look at the Demo Site in IE8 everything aligns properly.
If you could take off the background image and see if that makes the icons position properly. Also, you may want to use the Additional Business Info section to put in the phone number and email, that way it gets picked up by search engines and is clickable on mobile devices.
The other option is to add a width to that area. You can do that in Pagelines --> Site Options --> Custom Code. And try,
#page .section-business-branding .business-info {width: 160px;}
As far as I am aware there aren't any issues between the navbar and Business Branding. It seems Menu showing happens whether Business Branding is in the header or not. As Rob suggested, the Browser Specific CSS plugin is great for taking care of IE 8 issues. So, if you need to but a width on the area and you use the browser specific plugin then you just add .ie8 to the beginning of the css.
Let me know if any of the suggestions solved the issue.
Ellen