@Laura7046 Answer to Question 1: Real service dogs do not have "certificates".
If I ask a guest if their "service dog" has a certificate that they can take a picture of and send to me, and they do, then I know that it is a pet or an ESA. If they send me a picture of their animal in its "service animal vest" (as available from Amazon) I know that it is a pet or an ESA. When they read my Pet Rules where I state that the animal must be crated if left in the cabin alone and they protest that their "service animal" is perfect if left alone I know that it is a pet or an ESA.
Owners of bona fide service dogs that I have hosted have been up front about their animal and the duties it performs for them. These owners will search for a property that accepts animals before even considering or speaking to the owner of a No Pets property.
Answer to question 2: No, you do not have to accept the reservation. Be aware, however, that if you do not accept Fifi or Fido that you may be accused of discrimination by the bogus service animal owner and may be vilified by the animal lovers on this forum who cannot believe that there are property owners who won't accept animals.
P.S. You have a dog in your profile picture...therefore, I would assume that you accept animals at your rental property.