I want people to be logged in to book rooms. When a registered and logged in trying to book the registration form contains fields for the reservation. But if you are not logged in these fields are not shown.
The fields are of course already completed so you do not have to fill it again.

I'm sorry but I don't understand exactly. You can in component config set that customer must be logged. Then each customer has registration with personal data and reservation form is filled by this. On your print-screen is edit page of reservation for admin no for customer. Customer can't fill reservation data as from/to, prices, status etc.

But here the customer has allready filled ot the reservation info before he comes to this page. The info about the Capacity and price should not be available. And all the other info (Is Recuive, Status and payment) should also be hidden.

Hello,
I am not sure you have read Jiri's comment carefully - he wrote this is the Administrator's view, not customer's view.

So make sure to be logged as an user, who is just basic "registered" user, not with Manager or Administrator permissions.