Items reaching a Black Hole's Event Horizon seem to be frozen in time from the point of view of an outside observer. On the other hand, Black Holes collide and merge, in finite steps, producing gravitational waves observable to outside observers. How is it possible these two facts not to contradict each other?
I don't know if this question is a good fit for the Stackexchange format, because it's a complex topic that would require a lot of discussion. But I'll try to provide an answer.
I think you're getting the wrong ideas from the image of the event horizon being frozen in time for the remote observer. While this is true, it also means the remote observer never actually gets any information from the event horizon proper.
If you're a remote observer, and you see any change that happens related to a black hole, by definition that change is not happening at the event horizon or inside it. It happens outside that region. The event horizon might as well not even exist from this p.o.v.
The merger of the two black holes is what the remote observer sees. But a hypothetical local observer, inside the event horizon, would have a different perception.
For the local observer, the whole history of anything outside the black hole takes place in an instant. The whole evolution of the universe, including the black hole colliding with another black hole, and the resulting object evaporating via Hawking radiation - all this stuff happens in an instant.
You really need to think of it this way: the remote and the local observer experience two completely separate realities, where the flow of time in one is completely disconnected from the flow of time in the other.