It is 40° below (zero) this morning. Celsius or Fahrenheit? Both.
What is the temperature now?
[ Minus 5° ] [ Negative 5° ] [ 5° below } (zero)
[ 9° ] [ Plus 9° ] [ 9° above ] (zero)
"Twenty degrees below" is pretty good American English, anyways, without the "zero," which should be written out. Actually "twenty below" is by far the most common variant.
In Russia people usually say "минус двадцать" and it is enough, it's pretty understandable.
Important distinction to make though. Just about every country outside of the US uses Celsius so 20 degrees below freezing isn't the same as 20 degrees below zero [degrees Fahrenheit].
You are correct, it is genitive plural. The nominative singular form is градус.
You can easily find this yourself, actually. There are any number of sites available, but I like this one: http://www.morfologija.ru/%D1%81%D0%BB%D0%BE%D0%B2%D0%BE%D1%84%D0%BE%D1%80%D0%BC%D0%B0/%D0%B3%D1%80%D0%B0%D0%B4%D1%83%D1%81%D0%BE%D0%B2
The sentence does not state the scale used;). It would be «по Цельсию»/«по Фаренгейту», by the way.
I live in a desert that is normally around 100 degrees Fahrenheit (37 Celsius). This -4 degrees Fahrenheit (-20 Celsius) is incomprehensible to my mind.
Three times I had the chance to watch friends who were seeing snow for the first time or experiencing minus temperatures for the first time. It was a pleasure to watch them and to see and hear the reactions. Two girls who saw it snowing for the first time were dancing around and catching snow flakes and one said: "I thought it was like a refrigerator. But this is soooo much better than a refrigerator!" :o)
The word "minus" has a number of different grammatical functions in English:
"The word minus is a conjunction when used as a mathematical term for the difference between two numbers.
"It can also be a preposition, and adjective and a noun." https://www.answers.com/Q/What_part_of_speech_is_minus
Here I think it's an adjective modifying "twenty degrees". It's not a mathematical function. Or maybe it's a preposition. It's not a noun here. (Example of noun: "Lying to the FBI is a real minus for your future plans.")