The issue with the duplicate images has been fixed. That was a bug in the theme.
I see that you've marked two posts as sticky and have created a page called "Home" that uses the Showcase template. There are a few more steps you need to take to get the template working on your site:
1. In your Dashboard, go to Settings > Reading
2. Under the "Front Page Displays" section, select "A static page". Then from the drop-down box, select that "Home" page you created that's using the Showcase template. Pick another page to serve as your blog page.
3. Save your changes and view your site. You should now see the Showcase template as your Home page, and the slider should be active.
Let me know how this works for you.
If you'd like images to appear in the slider with your posts, you can add featured images to your sticky posts. The featured images must be at least 180 pixels wide.