I have a question.
"There is no cat in this park."
"There are no cats in this park."
Which is the correct sentence?
The normal, standard, and expected form is to use the plural form with the negative.
There are no cats.
However, if you need to be very emphatic, there are times when the singular would work.
A: I saw a cat
B: There are no cats here.
A: Look, right there. It's a cat.
B: No, it's not. That's not a cat. Really, there are no cats here.
A: I'm looking right at it. It's a cat!
B: I'm telling you, there is no cat here! That's my purse! God, buy some glasses, would you?!
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.