Is there a way to add columns and headers to the dual list box? I would like to display more information than a single column.

You can set multiple columns via

  AdvDualListBox1.LeftList.Columns: integer;
  AdvDualListBox1.RightList.Columns: integer;

I'm not sure where you want to see headers. 
There are labels you can show on top of the lists via:
  AdvDualListBox1.LeftLabel.Caption: string
  AdvDualListBox1.RightLabel.Caption: string