Again, the “output” of the SP is not axons, it is activated minicolumns. This enables other computations within the minicolumns to occur through distal connections like temporal memory. I know you don’t like the videos, but I talk a whole lot about this throughout them. See especially Cortical Circuitry for examples of how this computation is general and can be doing different things depending on how layers are connected up. This is more formally defined in the paper A Theory of How Columns in the Neocortex Enable Learning the Structure of the World.
No, SP and TM happen within the same layer. TM requires SP.
That example is fine. I did not realize it had different settings. The sparsity is usually configurable, and never as low as 0.0063. In NuPIC we keep it at 2%, and it is controlled by an SP parameter called numActiveColumnsPerInhArea , which specifies how many minicolumns will be activated at each time step. I am not sure how this is controlled in htm.core. Maybe @David_Keeney or @dmac can say.