You can do all of this from within Q2A, no need to mess with the WP dashboard...
Question moderation is already customizable based on WP roles
status of questions and answers could be implemented for the Q2A dashboard
access to wp-plugins is possible, since you have access to all of their functions. Check out the buddypress plugin for an example of this.
Scheduling is easily done with a Q2A plugin.
The only way to do what you are proposing is to create a wordpress plugin... interesting, but doesn't seem worth it, when Q2A already has a great plugin system of its own.