When creating your “add to cart” links, you must call the category and code. ie. http://yourdomain.foxycart.com/cart?code=my_downloadable&category=downloadables
No. The download links are added to the receipt page and to your receipt emails. Just make sure you style those and you'll be fine.
http://yourdomain.foxycart.com/cart?code=my_downloadable&category=downloadables^^receipt^^ placeholder is set in your receipt email templates. (It's in the default templates, if you're worried.)You could conceivably use the FoxyCart XML datafeed to build your own download management piece. If you have many, many downloadable products, or very large files, this could be an option worth exploring.