Is spørgsmål also plural?
Yes, mål doesn't change in it's plural form, so words ending with the word "mål" tend not to change in the plural form :)
Does this change if the word is definite?
The plural definite is different to the singular definite, yes.
et mål, målet, flere mål, alle målene
So "mål" is one of the few irregular words in Danish.
It's interesting that this word becomes regular when in plural definite version: "spørgsmålene"
What is wrong with putting the et in the sentence. Har du et spørgsmål?
"har du et sporgsmal" = do you have a question
Sporgsmal is not plural for word questions, you should correct it
sporgsmal sound like a new type of alchohol