1) you need to add Populate list from array behaviors to the onload event of the body tag and Set Selected in list behaviors for the 2 child lists to re populate then with the values that correspond to the parent list selections.
2) does the document_categoryID need to be a multiple select list? do you need to be able to assign multiple categories?
if so, you should be using a linking table for the document category and the manage relational table behavior to store the categories selected.