How do I embed a custom node creation form inside a view
As you're using plain php (not really bestpractice) you can code it out yourself there, having a select changing a query-parameter for your view (self made contextual filter ..).
A more sophisticated approach would be hooking your view, hook_views_pre_render:

This hook is called right before the render process. The query has been executed, and the pre_render() phase has already happened for handlers, so all data should be available.
Adding output to the view can be accomplished by placing text on $view-&gt;attachment_before and $view-&gt;attachment_after. Altering the content can be achieved by editing the items of $view-&gt;result.

Or create a custom page-callback (see hook_menu),
where you embed the view and add the form regarding your query param (or uri param).
You can check permissions with user_access.
You won't need to enable php execution with these approaches !