1) Yes, you can add more schools after you e-submit the application.
2) Most schools have supplemental essays, but not all of them do. You just need to do some research on the schools and their supplemental applications.
3) It does depends on the school application deadlines. Every school has different application deadlines from as early as the beginning of November to March of next year. Thus, you need to do some research on the schools and their application due dates. If you submit your application at the end of summer and the due date isn't until March of next year, then it's pretty early. If it's due in November and you're submitting the application in August/September, it's fairly early. 😀