question a):
"Is "fish are jumping" in the song "Summertime" a correct grammatical construction?"

answer:
no, it isn't correct!

"The plural of fish is usually fish, but fishes has a few uses. In biology, for instance, fishes is used to refer to multiple species of fish. For example, if you say you saw four fish when scuba diving, that means you saw four individual fish, but if you say you saw four fishes, we might infer that you saw an undetermined number of fish of four different species."
https://grammarist.com/usage/fish-fishes/Fish vs. fishes

question b):

"Plural of fish is fishes, right?"

Answer: 
no, this is wrong.

"the usual plural form fish is Fish. The older form, fishes, can be used to refer to different kinds of fish."

https://www.oxfordlearnersdictionaries.com/us/definition/english/fish_1
question c):

"...Or if it's fish as general substance then I would expect "is". Or I missed some subtlety?"

answer:

yes, you've missed somethin subtle... (as many others - who might have thought,
"fish are jumping" was afro-american English like: "Bess, you is my woman now!"
whereby here "are" is the 2. person singular and not 3. person plural.
(I think, this latest reference/personal experience must be aloud in this context!)