Sheets of fresh pasta sticking together
You may just be cooking too much at once.  When I make lasagna or rolled pasta, like cannelloni, I cook 2 to 3 sheets at a time, building my lasagna (or filling the pasta) as I go.  I remove the cooked sheets to a clean kitchen towel.  Proceed with the construction when they are just cool enough to handle, then add more fresh pasta to the cooking pot.