The header titles are all hardcoded inside header.php.
Posts that are shown on the homepage must have at least one of these two categories:
This means that Upcoming posts, by themselves, will not show up on the homepage. This is intentional — this way, the homepage will not be littered by multiple "upcoming" posts unless the author chooses so. Why would anyone want to see more than one upcoming post, especially if the "upcoming" post was written three weeks ago?
The number of posts to be shown is set in index.php.
How to write posts can be found in the sidebar.
Comments are driven by Disqus. You can modify how many are shown (and the format of it) in sidebar.php.