Are both sentences correct?
We attach our cheque for $100 which represents payment to your company for expenses on the project.
We attach our cheque for $100 representing payment to your company for expenses on the project.
Your check does not need to "represent" anything.
Our check (checque) for $100 for project expenses is attached.
If you're using U.S. dollars, then spell it "check."
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.