CheeseRex on "Replacing Category with Featured Image"

http://ednewsri.org/

Here is the ideal

My biggest desires are to

1) replace the green block category with a featured image (The category title with the little stripes that match the header), but not have the featured image in the post.

2) move the blog title up so it's next to the category block / image.

I've figured it all out so far, but hit a wall here. Any ideas? Thanks!