Oxaloacetate contributes to fatty acid synthesis, but it’s not a lipid, because, among other reasons, it’s not hydrophobic. This is also why it cannot cross mitochondrial membranes. Glucose can be synthesized from glycerol, but this process occurs via dihydroxyacetone phosphate, and doesn’t involve oxaloacetate. Oxaloacetate is synthesized from pyruvate, which is the end product of glycolysis, so oxaloacetate cannot be an intermediary in glycolysis. However, lactate can be converted to pyruvate, which is the principle substrate for gluconeogenesis (sometimes called “reverse glycolysis”). In gluconeogenesis, oxaloacetate is an intermediary in the conversion of pyruvate to phosphoenolpyruvate, and so that makes it an intermediary, too, in the synthesis of glucose from lactate.

Futile cycling occurs when two metabolic processes occur in opposite directions, and thus result in no net change. This is very wasteful, and not ideal. The only example of the answer choices of metabolic processes occurring in opposite directions is glycolysis and gluconeogenesis occurring simultaneously. Other possible examples could include: glycogenesis and glycogenolysis, beta-oxidation and fatty acid synthesis, etc.

Gluconeogenesis occurs in times of starvation, fasting, and low access to sources of glucose. This is the cells way of creating its own precursor when none is available, albeit at a high energetic cost (one cycle of gluconeogenesis can cost 6 ATP). Thus, it is untrue that gluconeogenesis occurs during high consumption of carbohydrates and fatty acids. Each other selection is true regarding gluconeogenesis. 

The Cori cycle comes into play during anaerobic conditions; where lactate from glycolysis travels from the muscle to the liver to be converted into glucose via gluconeogenesis. The glucose is then sent back to the muscle to be used for energy. Note that some of the lactate that is converted into glucose can be stored as glycogen in the liver, but glycogen is not transported from the liver to the skeletal muscle. 

In the absence of oxygen, oxidative phosphorylation cannot be used to produce ATP, so glycolysis becomes the primary source of ATP for the cell. The importance of lactic acid fermentation is that it replenishes cellular  for the glyceraldehyde-3-phosphate dehydrogenase reaction, which precedes the ATP-producing steps. Without lactic acid fermentation,  concentrations would become too low for the glyceraldehyde-3-phosphate dehydrogenase reaction to occur, and the ATP-producing steps would not continue to be reached. 

When glucose is fermented, it forms the product lactate.  Lactate can then continue on to be fermented to acetate. However, the other answer choices do not represent the correct direction from reactant to product in fermentation. In some organisms, ethanol and carbon dioxide may be produced via fermentation, but carbon dioxide is a byproduct, not a major product in these organisms. 

NADH is, under aerobic conditions, returned to  when it has its electrons taken in the electron transport chain. However, anaerobic conditions disallow this from occurring, and so NADH will build up in the cell. Fermentation is a pathway that allows pyruvate to be converted to either ethanol or lactic acid (depending on the organism) in order to regenerate the supply of .

Fermentation take place when there is a lack of oxygen in a cell. Without oxygen, the only process that can create ATP from glucose is glycolysis. However, NADH is created during glycolysis, and must be turned back to  in order to continue metabolizing glucose with glycolysis. Fermentation, therefore, has the main responsibility of regenerating .

As alluded to in the question stem, an abundance of oxygen allows aerobic respiration to proceed. This allows glucose to be oxidized completely to yield a high amount of energy. In contrast, when oxygen is scarce, cells revert to an alternative method of producing energy, but one that is far less efficient. This is known as anaerobic respiration.

Though there are different types of anaerobic respiration, the one relevant to this question is lactic acid fermentation. In this process, the pyruvate coming from glycolysis is converted into lactic acid. When this happens, NADH is also oxidized back into its non-reduced form. This is the reason why fermentation occurs. If all of the cell's NAD were to be in its reduced form, then there's no way that glycolysis could proceed. Since glycolysis doesn't rely on oxygen, this is the only pathway to provide a stable energy source during oxygen deprivation. So in order to regenerate the  needed for glycolysis to continue, it needs to donate its electrons onto pyruvate, which produces lactic acid.

Because the sprinter is exercising at a high intensity, his body is metabolizing its fuel under anaerobic conditions. Lactic acid fermentation is the conversion of pyruvate to lactate, and occurs only under anaerobic conditions. Glycolysis always occurs under anaerobic conditions, and glucose needs to be broken down to fuel the sprinter. The Cori cycle is the process that describes anaerobic metabolism on a larger scale (the conversion of glucose to pyruvate, to lactate, and back to glucose). Finally, because the athlete is using up his glucose, glycogenolysis will occur in order to convert some of his stored glucose (glycogen) to blood glucose.  

The only answer choice remaining is gluconeogenesis. Gluconeogenesis and glycolysis occurring at the same time would be called a "futile cycle". They are opposing pathways, and if one is occurring, there is no need for the other to occur, that would be wasteful. We already established that glycolysis was occurring, so it is unlikely that gluconeogenesis would also occur.