The light from the universe outside the event horizon of the black hole should be visible as a small disc or point light source in the direction facing away from the singularity.

This will happen even before you reached the event horizon. You do not need to cross the horizon to see this effect. At ergosphere distance the BH will cover half of the sky and closer to the BH the BH will cover greater part.

So one can assume that we are just outside the event horizon. And this is true: if the space is de Sitter we are just outside the cosmic event horizon, whether it is BH or not. For a distant observer we seem to be sticked to this surface and time-diliated.

The light from the universe outside the event horizon of the black hole should be visible as a small disc or point light source in the direction facing away from the singularity.

This will happen even before you reached the event horizon. You do not need to cross the horizon to see this effect. At ergosphere distance the BH will cover half of the sky and closer to the BH the BH will cover greater part.

So one can assume that we are just outside the event horizon. And this is true: if the space is de Sitter we are just outside the cosmic event horizon, whether it is BH or not. For a distant observer we seem to be sticked to this surface and time-diliated.

As this "BH" evaporates (via de Sitter/Hawking radiation), the diameter of the cosmic horizon will become smaller and the temperature will rise.

But we will never cross the horizon: we will be ripped before. This is called "Big Rip" scenario. We will experience the same what experiences an observer trying to reach a black hole: he will finally see a great explosion when the BH radius will reach zero.