In a functionalist society, do people need to agree within the society, or is it that they perform the actions in order to conform?
In my opinion, the functionalist perspective in sociology tells us nothing about why individual people act in the ways that they do. Functionalism is about the society as a whole, not about the individuals.
So, for example, functionalist theory says that crime and deviance exist because they help to define who we are. We define who we are by saying who we are not -- by saying "those kinds of behaviors are criminal or deviant; they are not acceptable to us."
But this does not say anything about why the individual criminal commits a crime. It only speaks about why crime is "important" to our society.
Society viewed by the functionalist is a system of parts each of which affects all the others and changes the society as a whole. No part can work in isolation. To maintain order and stability the actions of each part play an essential role. There is the concept of totality, society as a whole is dependent on the actions of each of the parts that constitute it.
Due to this it is unattainable to find a perfect working system with no conflicts. With each part of society working in a manner that is best suited for it, conflicts and instability is bound to arise and has to be dealt with an appropriate compromise made by each part.