I cannot reproduce.

Layer > Delete Layers (YR) deletes all selected layers (one or multiple)
Layer > Edit Layer (YE) edits the active layer (always one)

This is expected behaviour for both tools as one can delete multiple layers at once but one cannot edit multiple layers simultaneously.

Is this what you meant?

I'm talking about shortcuts. The context menu (right click on layer in layer list) works!
If the layer is "only" active (gray) a shortcut will work. If the layer is selected (blue marked) it won't work. Note: If I select a layer to make it the active one it will automatically mark (blue) the layer too. Shortcut YR will not work until I deselect the layer to make it "only" active.

Can you check your preference:

Edit > Application Preferences > General > Keyboard > Enable keyboard navigation in list widgets

If this is checked, shortcuts will only work if the keyboard focus is not in the layer list or block list. If a list has the focus, the keyboard can be used for list navigation instead. For example, "Y" will move to the first layer starting with "Y", etc.

Yes - it was checked. I unchecked it and now it is working. Thanks - I learned something new. ;-)

I tested the setting with the other mentioned issue regarding Y+ and Y-. That doesn't works. :-(