Your dog not eating can be a sign of serious internal complications. When my dog stopped eating, we brought him to the vet after a couple of days and were informed that he had fatal liver cancer. Of course, your dog may just be sick, or nervous if he/she is in a new environment, but you should see a veterinarian anyway just in case.

Yes, you should let your dog eat grass. Dogs normally eat grass because they are having stomach pain and want to throw up, so if your dog is eating grass regularly, there may be an issue with its diet or it may have some kind of stomach complication. If this behavior continues, definitely go see the vet.