Thanks for the screenshots… hard to say what is causing it, but my guess it could be the plugins being used. For your screenshot 1, it looks like the plugin containers for it’s content is not clearing surrounding elements within the page. This is usually done with a “clearfix” which most developers should know about.
It’s also true that every theme out there is not coded to work with the 10’s of 1000’s of plugins (and vice versa), so sometimes both may not play nice when installed. Case in point, I have a customer who experienced crazy things happening in her site with the theme she was using, and it turned out it was the social plugin she was using. She tried the plugin with the default WP theme and sure enough, it was causing issues there too.
With Luminescence, it uses a tricky script to keep the sidebar column and the content column equal in height, and sometimes that can cause some conflicts too.
So with that being said, what happens if you use the plugins you have but switch to the default WP theme, such as Twenty Thirteen or Fourteen?