P: Use Erasure tool as a brush

If a Brush was created with »Include Tool Settings« one can override that setting with another Tool by cmd-alt-clicking it in the Brushes Panel. 

Saved Tool Settings are indicated by a tool-icon in the Brushes Panel. 

You can change the eraser tool from a block to a brush on the tool options bar at the top of the window. Please advise if I misunderstand your questions.

warmly/j

»I would really like to be able to use the erasure tool with the functionality of the brushes - so that you can erasure with chalk structure, or ink lines, aquarelle etc.«

That seems to be possible already, what is the actual problem you are having? 

Could you please post screenshots with the pertinent Panels (Toolbar, Layers, Brushes, Brush Settings, Options Bar, …) visible? 

With the most recent versions of photoshop one can use the Brush Tool as an eraser by pressing the Tilde key ~

to erase and release to paint.

From this page under New Shortcuts:

https://helpx.adobe.com/photoshop/using/whats-new/2020.html#other-enhancements

"Paint and erase with the same brush

Use the ~ tilde key (below the escape or Esc key) to toggle between painting and erasing with the same brush tip."