Note that the cloudiness parameter is scene-based meta-data so it is only approximate (e.g. for an area of 100x100 km). Find here information how to do AOI-based cloud filtering: https://www.sentinel-hub.com/faq/best-way-do-cloud-filtering-specific-aoi
Sentinel-2 L2A data (available in Europe since March 2017 and globally since December 2018) do contain cloud shadow data as well and you can include them in the same algorithm as described above.
Note that we do not process any data, we download the data processed by European Space Agency, including information about clouds, cloud shadows, etc.
Thank you again for your answers!
One more question about variety of data types one can get using Sentinel Hub API. Here I mean different pre-calculated indices such as NDVI, EVI, images in different wave band which depicts objects in True Color and False Color.