When I click on any of those Gallery thumbnails, the Image Carousel opens with the image on a black background and I can scroll through using the arrows on right and left.
The images that have been inserted individually at the top of the page will not open in the Image Carousel when you click on them because when you inserted them, you linked them to their image attachment page Because you've done that, and those same images also appear in the Gallery at the bottom of the page, anyone clicking on the top images can browse through the attachment pages for all the other images in the Gallery as well.
If you want to stop this behavior, change the Link URL for the individual images at the top part of the page to "None" or if you want to keep those images out of the Gallery, you need to use "excludes" in the Gallery shortcode. See here: http://en.support.wordpress.com/images/gallery/ under Gallery shortcode. Any editing of the Gallery to use excludes has to be done in the Text Editor.