After ordering the products, you have to log in, click on the YOUR ORDERS menu item in the topbar, then choose the order number, and click on the file name in the files column to download the file. Don't worry about unfinished orders, you can start the ordering process from the beginning any time.
The differences between the professional and the free versions are generally the number of module positions, the dropdown menu, more customization options, like the image logo option, additional blog layout, module styles, and the number of social icons.
The product pages generally have a link to a page that contains instructions about setting up the template, like parameters, module positions, menu setups. You can also find these instructions on the demo sites, just click on the top menu items of the demos.