Hierarchical Drop Down Menu for Products


I anticipate having a large taxonomy of products. In creating categories, I have created a three-level hierarchy as follows: category > subcategory level 1`> subcategory level 2.


1. In the Dashboard area when creating a new product, how do i display the categories/subcategories in a drop down menu/submenu when selecting a category to post the new product?
2. How do I dynamically display the appropriate subcategory level 1 when the Category is selected? For example, if there are 3 main categories (such as Birds, Mammal, or Fish), and I click on Birds, only the subcategory menu for Birds will show (i.e., bluejays, sparrows, etc.)
3, How do I allow up to three categories/subcategories to be selected for a product (as shown in the attached image)? This is for cases where a product can be appropriately categorized in more than one category.