Can forms be added to a page of quick tabs?
Should be possible via custom code. You can read up on how to build quicktabs programmatically here: 

https://www.drupal.org/node/2119625

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.