I am still not sure whether I understand enough what you want to achieve and I do not have knowledge what elements exist in ArchiMate and what there meaning is.
However whatever element you use( e.g. in a diagram) is based on a “Base Class”, e.g. your ArchiMate_ApplicationComponent” is based on Component. You can find out this by deleting the Stereotype and reopening the properties dialog where in the frame header now is Component rather than ApplicationComponent.
An element can have many stereotypes assigned to, however the first assigned is somehow master and e.g. defines the layout of the element in a diagram.
So if you define Base Class <all> that means your stereotype is assignable to any kind of element maybe already having some other stereotypes already.
If you want an element to look different you have to provide information about that. In virtually all cases (some minor exceptions exist) to say "that there is something different, additional,…"you have to use a stereotype and to make the element look different you can define colors, images or shape scripts.
This statement below gives me the feeling we all talk about different things.
No. I want to reuse the Archimate Component shape and the BPMN Swimlane shape. Is reusing not possible? Do I have to create new shapes, although they are already there?
I did not found the ArchiMate Swimlane in my tool boxes of ArchiMate but Swimlanes you could classify under context menu “Advanced/Instance Classifier.
(maybe that is just what you are looking for)