Is there a payment function for my customers so that appointments are paid for immediately?

Yes, Calenso supports online payments. All you need is a credit card and a Stripe or PayPal account if you wish to pay by credit card. With a bexio account, you can even issue invoices to your customers for the services they have booked.  Calenso also offers you the possibility of issuing discounts which can be used during the payment and booking process. You can find out more about online payment here.