Essays for what? The application essays to various schools? No, you won't need to do that. I suggest you read the webpage of the schools you are going to apply to first to get a clear idea.
As for the GMAT score, you'll have to indicate anywhere upto 5 schools you want to send your SCORES to, and you'll get an option at the end of the test if you want to accept/cancel scores. If you accept, the scores will be sent to the schools you selected. Remember if you dont choose any schools, then later on you'll have to pay $25 per school.
Yes, the essays are vastly different from one university to another. Once again, I recommend that you look into the websites since these questions are easier understood by reading through the admission requirements on websites than anything else.
No you don't need to visit the schools, but sometimes it might be preferred just so YOU can get an idea of what the school is like and vice versa.
Hope this helps!