Is it possible to embed a content creation form in views header?
It doesn't have to be in the view header. Just place it block above the view and adjust the css so they sit together. 

If you use entity forms and entity form blocks, you can just place a block above the view block (or panel pane).

Rules will allow you to create a new node, set the current OG_context as the new new node's group and then redirect back to the same page or to the new node.