Couple of questions regarding graphics API?

I want to create a new API like DirectX. I have a few questions regarding this?

If I create a new API that works on PC and consoles, will my API will be allowed to run on PC and consoles(or they will force me to use like PSSL for PS4 and DirectX for Xbox etc)?

If there are no such issues, how can I create a Graphics API which will have its own API like DirectCompute etc ( link to starting point from which I can move on) ?

What I want is to directly access the CUDA architecture for nvidia ,CGN architecture for AMD etc?