Is there any way she can delete such posts or retrieve his profile or something?
There could be a simple way to execute a statement from mySQL manually, but I'm not sure if you will need this command? Is anyone from your client's area familiar with executing mySQL statements?
Unfortunately, if a profile has been deleted, there is no easy way left on forum to delete such posts.
the pre-moderation add on is for moderation of ALL posts?
Is there any possible moderation add-on just for member applications?
You may test on miniBB demo
how it works and you will see there are options for certain users,or new accounts which are added to the queue automatically, or for all posts - so it serves the purpose in various modes.