Does this support two way live sync with google calendar?

Does this support two way live sync with google calendar? Does the calendar in form block out time slots not available?

Unfortunately, form can only pass the date selected into a calendar, but it will not check slots available on the calendar. If you need to limit dates selection, I can suggest to take a look at Date Reservation widget, it allows to select every day just once. Then, you can conditionally copy selected date to hidden date picker field, which is linked to your calendar. This way, you'd get a limit for every day:

How-to-Add-a-Widget-to-Your-Form

We will be glad to assist if you need more help, just let us know.