Add Anchor point pen tool

No there is not.  It is a tool that is available in Photoshop, but not photoshop elements.  You screenshot shows a feature only found in Photoshop, but not Photoshop Elements. 

THERE IS ONE EXCEPTION:  TEXT ON A PATH.  You cant creat shapes, then edit the anchor points--- you can only edit the path that text will appear on.  You cannot add or delete anchor points (control nodes). 

ONE EXCEPTION.   

Text on a path.