The free-energy change for the oxidation of glucose to co2 and water is -686 kcal/mol, and the free-energy change for the reduction of nad+ to nadh is +53 kcal/mol. why are only two molecules of nadh formed during glycolysis when it appears that as many as a dozen could be formed?

In glycolysis 4 ATP are formed, but 2 ATP are used in its early steps. Glycolysis end products include 2 NADH, 2 ATP, and 2 Piruvates.  Glucose in Glycolysis is only barely oxidized

Explanation:

Piruvate is an organic molecule with three carbons with a great potential energy in its chemical bonds.  Glucose is broken in  2 piruvic acid (or piruvates) and still maintain much of the original energy of the glucose.  Piruvates are very reduced molecules

NADH is formed when NAD+ is reduced from glyceraldehyde 3 phosphate, when this is also converted into 1,3 biphosphoglycerate, previously.

In presence of O2, piruvate can be decarboxilated and oxidized forming acetyl coenzyme A and CO2, and 2 NADH.  In Krebs cycle more ATP and reducing power is produced (FADH2 and NADH).  And finally when electrons from NADH and FADH2 travel to O2 reducing it to H2O, with its concomitant ATP formation.  A protons gradient is formed  in this respiratory chain, that is responsible for the massive ATP formation in that stage

the answer is definitely c.

a polar bond is formed when electrons are shared unevenly between atoms