The icon with the frames shows / does nothing

This is used to show / hide guidelines on elements like tables, which without borders assigned, would otherwise be invisible.

the paragraph-icon shows (only?) nbsp

Exactly, this shows non-breaking space elements.

and for the block-elements I miss some tags like br and li and so on (maybe they are no "blocks" but nevertheless helpful).

It only shows block elements, and li and br are not block elements.

Any buttons you do not find useful can be removed from the editor toolbar in Editor Profiles -> Features & Layout.

at nbsp: "only nbsp" or other elements too?

Only nbsp. I'm not sure what else would be useful, especially since paragraphs can be shown with the Visual Blocks option.

at not block elements: kann other things like br and span also be displayed?

No, only block elements. Linebreaks are obvious as they shown with an actual newline break.