Is the buoyant force on an object the reaction force? Is the buoyant force on an object the reaction force for the force exerted by the objects on the fluid (Newton's third law)? Or are there two sets of action reaction forces? (objects force and reaction, buoyant force and reaction)
 A: A fluid exerts a buoyant force on an object, and the object exerts a reaction force on the fluid (which causes some displacement of the fluid).
A: Suppose you have a weightless box that is 1cm square.
Suppose you push it down into some water, to a depth of 1cm.
Since you are displacing 1 cc of water, the weight of the water you are displacing is 1 gm.
So you are pushing down on the water with a force of 1 gm (I know that's mass, but bear with me).
The water is pushing up against you with a force of 1 gm.
That's the reaction force against your push.
That's also the bouyancy force.
A: Action-reaction language is poor because it implies that one force (the reaction) arises as a result of the other (action). This is not true. Forces (in inertial reference frames) are interactional, i.e., they are simultaneous, both arising from an interaction of objects with fields. One might say that each force is both an action and a reaction, if you insist on using Newton's words. Keep in mind, he simply used those words to signify  their mutual existence, and not the order in which they happen. One could also say neither force is the reaction.
The buoyant force is actually a net force due to the interactions of small area elements of the object with the liquid molecules. There is a Newton's 3rd law pair of forces at each interaction point 1) force on the fluid from the object and 2) force on the object from the fluid. Neither is the reaction, nor the action. Neither you, nor I, nor "any wizard that ever was" (Wicked) is ever going to uniquely define which force caused the other.
