> Can a storymap be viewed by someone without an ArcGIS online account?
Of course, when publishing a story, just choose to share it with "Everyone."
> How do I embed a storymap on my company's website?
First, be sure the story is shared with Everyone, as described above. Then share the link to the story with your website administrators. They will create some HTML code called an iFrame using the story link and add that to the website. This will embed the story in your website.
You can also simply link to a story from your website, too. By that I mean provide a button or link (a text link or perhaps even a link attached to a screenshot), to open the story in a new browser tab. Linking is recommended if there isn't sufficient space available on your website page for readers to properly experience your story. It also can be much better if you have a lot of people visiting your story from mobile devices.