Hello, wordpress themes by default don't show other items than posts in search results, I think that your events plugin added the functionality to the search to display it's own post type (tribe_events), however the theme doesn't know how to do it since it was not designed to show anything else but posts, with the products it's the same issue, first we need to tell WP to also display products in search, and then make the modify the theme to display them correctly.
You can see here, if we overwrite the post_type parameter
[login to view URL]
They display fine, so no further work is required here, however for events we still need to modify the theme.
I can modify the theme right now if you want, let's talk in chat and fix these right now as they aren't such a big deal.
Kind regards, Cristian.