Hi,
To tailor screenshots you can crop them in a paint program like Windows Paint or Paint.net. The Story Map builders don't have a crop function for images so it is best to make any modifications to images first before using them in a Story Map.
The content in ArcGIS is crawled by Google but searches usually need to include 'ArcGIS' as a search term, and they tend to take people to the ArcGIS Online item details pages for the content, rather than directly to the map or app that the item details page represents. To improve your content searchability, be sure to include a good set of search tags, a brief summary and description in the item details page for your Story Map. However for best searchability/SEO, we recommend that if possible you add a link to your story map into a web page, or embed your story map in a web page, that your readers will be more likely to find via search. So if you work for a city and your Story Map is about parks in the city, feature that Story Map on your city's official web page about parks. So when people do searches about parks in the city they'll find that web page and also your story map. Similarly if you have you have a blog or your own website, feature your story as content in that media too.
Rupert