Custom Menu limitation, adding post count, etc

I’ve created a custom menu under the “Menus” page or wp admin, and I’ve noticed a few limitations.

First, there isn’t a way to add the post count to the categories added to a custom menu.

Second, for any category added, there is no way to indicate that I want to display it’s sub-categories (ie, a hierarchy).

Third, isn’t there a way that I want all sub-categories of a specific parent-category to be displayed? Right now, if I add a new sub-category, and have to remember to update the custom menu. It would be more convenient to just specify a root category (and maybe an option to only show the sub-categories).

Is any of this possible with custom menus, or are they meant for very basic menus?

In addition, I’d like to note the following: if I have two sub-categories with the same name but under different parent-categories, I’d differentiate between the two when selecting from the “Categories” panel to the left (parent is not indicated).