I can't seam to confirm either of your issues on a clean install with CB 1.7.1 in IE8 Rendering with IE9. How exactly are you testing? IETester? IE8? IE9 with IE8 Rendering? It's very likely there are other JS problems present causing subsequent JS to fail. Please restore curveycorners and let us know once done so we can see what error is happening exactly.

I have restored curveycorners but cannot let it last long because as you can see on home page, the modules disappear on top and bottom. I f we remove the script, all is ok

I see no errors in the console so don't see why the two would be conflicting in that manner. Nor do I see any CSS issues at a glance. It's worth noting that it works fine in IE9. It disappears after the page completes loading (shows until then) meaning it's JS related, but I've no idea why the module is for some reason stopping its display. Perhaps the developer of the module may have a better clue as to why it's doing that. There's simply too many modules for me to find where those 2 header modules are even coming from so I can't review if it's a setting within the module that could be causing a conflict.

Further go to activ-ha.com/userprofile/demo.html and click on a deal with IE8 and you will notice that the browser crashes then restore a new tab with the proper link clicked.

This seamed to work fine in all browsers. Able to provide exact steps to experience what you are experiencing? IE8 (IE in general actually) aren't known for their performance and reliability.