I think it depends. And by that, I mean it depends on what the reasons for us being designed were. If a higher power designed us for the purpose of worshiping it, then we're using food wrong and using the bathroom the wrong way. If an intelligent designer created us just to see what we would do, or because it was curious, then yes we would most likely have free choice.
No. Free choice/free will is a major component of 'intelligent design' or creationism. One of the most important and generally inviolable components. However free choice does include both natural and spiritual consequences here on earth and after all that has been intelligently designed ceases to exist.
Yes,if the designer preplanned our fate, such as Romans 9: 21 - 23. But if to see what we'd do, then in part since how he made us also reflects our ability to choose when in human form. It is still limited by the creator.