Hi Danielle,
1. A very similar example can be seen here. There is a tutorial on how to replicate that layout here.
You have multiple options here. One is to use the shorcode generator, and another one is to use the elementor blocks, and put the settings shortcode in one, and the search shortcode in the other.
I would probably recommend using the elementor modules, since you already using it and it might give you some benefits for editing margins/paddings etc..
2. You are looking for the results shortcode here. It allows you to position the results from below the search bar to a different position on the same page. You can place this shortcode in an elementor module (try text or shortcode module if exists), like the other ones.
For a similar layout, I would recommend using a search theme with the vertical layout. From the latest release you can also define multiple columns to it.
You can also display results initially with the auto populate feature.