got new 2 piece racing brakes rotors and those don't have wholes for retaining screws.

is it OK to user brake rotors without those screws?
no problems/damage possible?

the car is primary used for traking and spirited driving.

 

Yes, it is perfectly acceptable to run without those screws. They are there to help with mounting the brake assembly. It keeps the rotor flat against the hub to make installing the brakes easier. When the brakes are installed, they will hold the rotor against the hub if the screws are not there. Without them, install will be a slight bit more difficult because the rotor will move around, but it doesn't make it that difficult.

 

Better not to use the screws, in my opinion. All they do is rust in place and cause headaches. I've had to drill out a number of them on my S2000 and Accord. These days I leave them off. It's still easy to install the calipers and wheels even without the screws.

 

Pulled mine out the first time I had the wheels off. They are an assembly part, not one needed for operation.