Can I add the plugin to the Home page of my site?

The plugin has a shortcode so if the area in your preview is a widget area you can enter the shortcode there.
Alternatively, you can do_shortcode to add it to the HTML page template (https://developer.wordpress.org/reference/functions/do_shortcode/).
As the area on the page is quite small you might like to try using the map as a pop-up to save space like in this demo:

If you need any form fields added or removed, let us know and we can send you a custom version.