I have also been trying to find the descriptions as well as icons.

There is no call to get them, but there is a zip file containing all the weather code, their descriptions and icons as well as multilingual support.

Here is the link https://weatherstack.com/documentation

Search for current > weather_code to see for yourself (and download latest version) or just download from here https://weatherstack.com/site_resources/weatherstack-weather-condition-codes.zip

Cheers