Frustrated with Eraser tool! 2020

If you want help with the specific problems you're experiencing, can you show exactly what they are in images and perhaps deal with them one at a time? It's difficult to unpick that paragraph.

In general though, people familiar with pixel-based drawing encountering the eraser in Illustrator for the first time seem to often misunderstand what it does. It's also possible that with a better understanding of Illustrator in general, most people realise they don't really need the eraser for much at all, if anything.

I think to be comfortable with using the eraser you need to first be aware of the separate concepts of a path and its appearance. A path is a vector path that makes up the bones of an illustration, what you see in outline mode (Ctrl + Y). An appearance is anything visual attached to the path, such as a stroke, fill, or brush. Appearances in Illustrator don't exist as editable elements separate from the paths they are attached to unless you make them (i.e. Object > Expand/Expand appearance).

The eraser acts on paths, not appearances. If you have a specific art brush on a path (that creates a shape along its length), and you run the eraser through it, you now have two sets of that art brush:

It won't cut 'cleanly' through the appearance, because the appearance only exists relative to a path -- and you have now made two paths.

Likewise, if you have a filled shape with a stroke around it, and you run the eraser through it, you now have two filled shapes with strokes around them. The eraser won't affect the appearance of the stroke, only the shape of the underlying path. Think of a router going through wood:

One of your problems was the eraser going through all layers instead of just what you have selected. It shouldn't -- if you have two objects, and only select the top one, the eraser should only affect that: