I take that back. NO, it does not address the first issue, because I have no control over the type of content that can be posted to Groups.  Just because I have site content like 'Recipes' (an outstanding module by Modzzz), doesn't mean I want recipes in a sewer workers group, or my communist transvestite bird watchers group... it just doesn't belong.  I can remove 'Recipes' from Group navigation menus easily enough, but placing the 'Add New.. content' block on the Group View page, there's the Recipe link big as life.   

Therefore, I must change my answer to No... it does not address the first issue.  Conceptually, the simplest workaround would be an "Add New..." menu item that works off the content types I have enabled on the Group menu.  It's a bit sloppy, technique wise, but perhaps something that could be done quickly, until a more permanent solution is crafted