Google's Structured Data Testing Tool will throw an error when validating JSON-LD if you do not include an image of the business citing "A value for the image field is required." The Google documentation simply describes the image field as "An image of the business." The tool will also throw a warning if a price range is not included, warning "The priceRange field is recommended. Please provide a value if available."
hCard does allow multiple personal profile links under rel="me". I wasn't able to find anywhere that said that this can apply to businesses as well. However, there was a post on Quora in which Dan Connolly says to go ahead and use it for businesses as well.
Schema.org has certain business types as children of the Organization specification. We have listed most of them above her, omitting some less common types.