Hi,
Yes – you can use the shortcode as a widget as well, there are widgets available for widgetized areas.
Unfortunately WordPress does not support multiple results pages, it is a core limitation. If you need a different layout based on the post types, that might get a bit difficult.
You can either try this experiment feature with Elementor.
Another possible way is to use the results shortcode as a makeshift results page.
Another possibility is to do some custom coding on the results page so that different layout is used for different parameters. WordPress unforutnately can’t have multiple results pages, always the same template file is invoked. However you can use that to programmatically check the query parameters and change the output programmatically depending on them.