Thanks for the report - the "object has no animations" bug has been fixed for the next build.
The fact deleting the last instance of an object in the layout does not delete the object type is by design. You are allowed to have a sprite object with no instances in any layout, for example. To properly delete an entire object type, you must do so via the object bar or project bar.
The issue with the delete key in the object bar was a window focus issue. IIRC, I did it because it was convenient in some cases... but I've put it back for the next build so the delete key prompts like the project bar does.