How can I avoid duplications

I need to create a form for enrollement with a time slot of 30 min per customer but I want date and time to become unavailable when someone registers

You can make use of our Appointment slot widget, that way, you can set how many slots are available, and when selected, the number of available slots will decrease after submit.

You can find the widget here:

https://widgets.jotform.com/widget/appointment_slots

Thank you.

Thank you. This is very helpful but I really need is that two people take the same time on the same date

You can achieve that using the same widget, you can add a slot for that time and date, and set the available number to 2, this way you will have 2 slots available for the same time and date. 

Thank you.