I have just used the 'Add New' button in the Appointments+ plugin backend.
The slots were definitely booked out, because when I went to try and make a booking for the same time in the front end, it told me the slot had already been taken.
However, I did not receive a confirmation email to the address I provided. I setup two different appointments, with two different email addresses and neither of them received a confirmation email.
When I removed one of them, I got a 'confirmation of removal' email - so it seems the issue is only with the initial confirmation email.
Please help, thanks, Phil.