@Kim:
1. You can reduce the margin bottom in the following css as per your need and then add it in “Appearance => Theme Options => Custom CSS” box:
.search-results .hentry { margin-bottom: 20px; }
.search-results .hentry p { margin-bottom: 20px; }
2. In your post “Botox for jowls, Ladies!”, you have split the content using more tag. So, edit that post and remove that more tag and it will show Read More. The excerpt content check the number of words before more tag and if it is less than the words setup in “Appearance => Theme Options => Excerpt/Mote Tag” settings then it will not display read more. If you are confused with more tag then read this http://en.support.wordpress.com/splitting-content/more-tag/
3. Search is not designed to display thumbnail. So, cannot add that. You might want to search for plugin to do that.
4. Go to “Appearance => Widgets” and then Drag and drop any widget you want to “Header Right Sidebar” which will replace your social icons