How can I add a simple node creation form to a page?
the only way I can see this being possible, would be creating a custom node/add page for your content (see How can I theme the template for edit or add a node for a specific content type?) and then using Panels to create a custom page with your node on top and then your view directly below.

I would be interested to know if anyone else has any better/easier suggestions of course. +1 for question :)