a) I selected Illinois and then also now selecting it as the Zone by clicking on the EDIT icon.. I then type in the pop up and putting a "check mark" in Illinois and it is "Published" and clicking OK.
You don't mention whether or not you selected Ilinois in the "tax category" and "tax rate" options of the tax rule that you created. If that's not the case, the tax won't be applied to the products.
Also, in your products you need to select the "Ilinois" tax category that you created.
By default, when a user didn't yet enter his address, the taxes on the prices are calculated based on the "main tax zone". If you select Ilinois, the taxes throughout the store will be calculated as if the current user was in Ilinois. So if you decide to show the prices with taxes on the products listings and/or the product page, the prices will include the taxes. If however you decide not to, then, regardless of the the way you configured the taxes, you won't see the difference on listings and the product page.