This strikes me as an issue between understanding these events from the point of view of an external observer, and a test particle or person falling into the hole. From the POV of the observer, your statements are largely accurate, for certain types of universes. For the test particle, there is no freeze frame, all proceeds normally.

The key is the Relative in Relativity.

Truthfully, there is no clear answer as to what a black hole has for an interior, or if it really has one. Holographic theorists would argue that the event horizon is the black hole, String theorists would argue that there is an interior, but no singularity. We just don’t know.