In The Giver what areas in life do the members in community have a free choice? What areas of their lives is tightly controlled?

More often than not, the people in the story's society have very little choice. The yearly ceremonies for children are a good example. When a child becomes another year older, they are given a new item or responsibility that they must take on. Sometimes, the age requires the child to give something up. For example, when a child turns eight, their comfort object is taken away. A society that demands giving up a stuffed animal on your "birthday" is an extremely controlling society. People are even told at the Ceremony of the Twelve what job that they are going to have for the rest of their life.
The best example that I can think of that shows the society allowing some individual choice is the volunteer hours; however, even those are somewhat controlled. The "volunteer" hours are mandatory starting at age eight, but the children are allowed to choose where they would like to volunteer. Most start volunteering for Recreation Duty. Eventually, a child will begin spending more and more of his/her volunteer hours at the job that they like the most. The volunteer hours are kept track of and tabulated at the Hall of Open Records, and those hours are used to assign the child's societal role at the Ceremony of the Twelve. In a way, this allows a child to "choose" their career path.