Store-Logic allows you to have as many categories as needed, there is no limit. However, we recommend not making category trees more than 5 levels deep for best practice reasons. If a user has to click five time to get to a product it makes the site hard to navigate and it is less likely customers will find what they are looking for.
Yes. You can discount all products in a category by a percentage by entering the percent of the discount in the discount field of the category Add/Edit screen.
Store-Logic allows you to create shipping rules that only apply to the categories you designate. So for example if you wanted to offer free shipping for all Mens Shoes, you would create a shipping rule to apply to this category.
For more information on how to set up a shipping rule based on categories go to the Custom Shipping Method page and read the Category section.