I want to create a page of quick tabs with some node editing pages, webforms and some admin pages as well regular static pages which just display information without any editing.
Is that possible?
Should be possible via custom code. You can read up on how to build quicktabs programmatically here:
For the node editing pages you will want to use the example for
Custom contents (HTML or renderable Array) on that page, where you get the form using the core function
drupal_get_form('node_BUNDLE_form') and add it as the "renderable array".
For the webforms you could try to work with the
Callback tab type, or again by loading the webform and building the render array.
For the static content i'd recommend to use nodes as this is always better than hardcoding things, so use the
Node tabs type.