Thanks for updating in!
1.) The blog index and post archives will use excerpts to display a summary text or the very first few words from your post. If you created a post with Cornerstone, nothing will display in the excerpts because all the contents will be wrapper with Cornerstone formatting shortcodes. To resolve this, you will have to insert manual excerpts for your posts. Please check out this link on how you can insert the manual excerpts:
2.) With regards to the post that has an Audio Post format,
Audio source missing means that you haven't added the audio code. Please edit this post and find the Audio Post Settings.
The audio post meta options can be found beneath the page editor in WordPress and will be labeled Audio Post Settings. Below is an image of what this meta box looks like in the WordPress admin area:
3.) That is because you add a code shortcode. Please only use the recent post shortcode in the text widget and no other shortcode.
[recent_posts count="4" orientation="vertical"]
Hope this helps. Please let us know how it goes.