From what i understood.

Electromagnetic radiation/photons, for a gravitational field, have basically just a gravitational wave traveling with them. The true origin of that gravitational wave is the accelerated mass at the moment of creation of the EM wave. In practice, its not possible to make EM waves with out that gravitational wave. Same thing with photons. Abstractly you could have naked EM waves, but that would be a pathological solution. Its right all this?

A gas of photons has the gravitational field of the sum of all its gravitational waves. This shouldn't behave like the exterior of the Schwarzschild solution. We shouldn't get newton at the limit from this. Right?

When a photon falls in a black hole.... Depends how we model matter in the singularity. If we consider that all the stuff are still there somewhere in the singularity. Then photons add momentum to a black hole, not strictly speaking mass. I mean, that if you change reference frame, so that the black hole is immobile again, you see again the original black hole. If you throw several photons, the momentum gets out again as gravitational waves....

I tried to read wikipedia on this, but it was too complicated. What i'm doing wrong with the above?