Newton's third law is defined as $F_{12} = -F_{21}$
Is friction a product of this law? For example, if I take my hand and slide it across the floor in the $+x$ direction... My hand exerts a force $F_1$ on the floor. According to Newton's third law, the floor should exert a force of $F_2$ on my hand, and $F_2 = -F_1$.
Is $F_2$ friction? Or is friction an additional force that occurs on top of $F_2$?
No, it's not a product (i.e. a result) of Newton's third law. The third law only says that the force of friction the floor exerts on your hand is accompanied by a frictional force of equal magnitude exerted by your hand on the floor. It doesn't actually explain why either force of friction has to exist at all. For example, your hand sliding on a frictionless surface doesn't have any friction (of course), but Newton's third law is still in force.
NO FRICTION IS NOT THE REACTION FORCE the frictional force provided by your hand on the table is accompanied by a frictional force exerted by the table on your hand. That is the reaction force here
Friction is a consequence of energy lost as heat whenever there is a relative motion between different components of a system. If a block of wood is pushed on a level ground the molecular bonds that cause adhesion at its interface with ground are constantly broken and recreated. This process generates heat.
At a molecular level, there is no friction. However when we consider macroscopic bodies, we ignore several degrees of freedom while considering macroscopic motion. Friction is due to the motion along these ignored degrees of freedom. (For example, while considering the motion of the block of wood, we assume that all particles of the block are moving in a single direction. While in reality, the molecules at the interface are being pushed around randomly. And of course, all molecules have a thermal vibration.)
Another example of friction could be a fluid in motion. Different layers of a fluid some times move at different speeds. The molecular adhesion leads to transfer of momentum across layers giving us the macroscopic concept of viscosity.
I know this post is coming way too late, but I think the underlying confusion behind the question is one involving fundamental forces. The question was whether friction, in a case like a hand sliding across the floor, is caused by Newton's third law. The answer should be: "No, friction is caused by the electromagnetic force". The third law pair the question refers to just happens to be made up of equal and opposite forces caused by the "facet" of the electromagnetic force we call friction (and there were already some answers given discussing this "facet" of the electromagnetic force). Incidentally, the third law pair of normal force of hand on floor with normal force of floor on hand is also a force pair of electromagnetic forces. Then there is the third law pair from the gravitational force: the gravitational force of floor (where by floor I mean earth) on hand paired with the gravitational force of hand on floor (where by floor I mean earth again). And finally, I would say there is the electromagnetic force of arm on hand paired with the electromagnetic force of hand on arm. (Obviously it is sensible to neglect drag).
