If the issue was the number of posts per page, the front page would display the latest post, not the other one, there would be an "Older Posts" tab at the bottom, and the monthly archive page would display the same number of posts per page.
Superhero has an option for "featured content": selected posts can appear in a full-width slider at the top. Check the demo:
The selection is based on a tag you specify in Settings > Reading, and the posts require a wider featured image than regular. So here's what happened: you haven't specified such a tag, so the theme automatically picked one of your tags; but since the featured image of the post isn't wide enough, the post disappeared instead of showing in the slider. Go to Settings > Reading, type something in Featured content > Tag name (type a number or whatever, just not one of the tags you're using), click Save Changes.
By the way, there's absolutely no point using a word or a phrase as a tag when you already use it as a category, plus doing so will lead to technical problems. You should delete these duplicates and create them again as either a category or a tag, not both.