Download all .7z files that came with your purchase, extract them using 7Zip, then add them to your asset library in Blender.

7Zip, a free and open source software, can be downloaded here: https://www.7-zip.org/

Here is a more detailed overview of the installation process: How to Install Foundations of the Earth

Yes, all Foundations of the Earth assets are compatible with both Cycles and Eevee. This includes not only the models themselves, but the utility node groups as well. The assets should look virtually identical in both render engines.

The most convenient way to use the assets is through Blender's asset library.
If you wish, you can also append and link assets into your scene via their respective .blend files.