All details such as date, time, duration as well as full name and email address will be stored in your JotForm account.
You can avoid conflicts by setting the appointment type as one-on-one so that a single user can attend the session. You can always limit the number of users who can signup for a particular time slot. With JotForm Appointment field, you can when, how long, and how often your appointments will be. If you need to schedule appointments, JotForm is the perfect tool for you. But I think your goal is a little more than that. You need to have an add-on - choice eliminator - which will allow you to unable a time slot if it's previously taken. You can create a google form with a multiple choice field that shows time slots for appointment times.
