You can use the like any other HDRI: Add an Environment texture to your background node in the would settings. Upload the HDRI into the environment texture.

Most of the shots in the trailer where shot with a relatively low focal length, like 20-35mm. Try changing the focal length for different results.
You can also try adding a mapping node and play with the z location value to change the size of the planet.

Working with such big files, like 8k and 16k can be quite heavy for your computer. I would advise to use lower res HDRIs when experimenting, and for the final render switch to the higher res.
Also, when trying out lots of different HDRIs, blender keeps them in the scene, which can cause problems. Purge all the unused images, for better performace.

Yes! As long as you dont just resell the HDRIs as they are, but use them in real projects or shots. For mor info, please read the license file delivered with the HDRIs.

Both EXR and HDR are 32bit images, which means you get a lot of Dynamic Range. The EXR files are a lot smaller then the HDR files, so I would recommend using them. In some Programs EXR is not supported, which is why I've included the HDR file format.
The JPG files are 8bit images, and are just meant as a backdrop, not for lighting the scene.

I intentionally did not include the sun in the maps, since you oftentimes don't want it in your shots.
Especially in 3D programs, this allows you to light your object with your own directional light, not having to worry about the rotation of the HDRI.