Are humans capable of both anaerobic respiration, and lactic acid fermentation?
Humans have no anaerobic respiration, if we define this as oxidation of a substrate with an external electron acceptor other than oxygen. In humans, the terminal electron acceptor in respiration is always oxygen, which is reduced at complex IV in the respiratory chain. Alternative electron acceptors are mostly found in bacteria and archaea.

I would call the anaerobic metabolism of glucose to lactate in humans a fermentation process. It consists of glycolysis, which converts glucose to pyruvate, which in turn is converted to lactate by lactate dehydrogenase. There is no terminal electron acceptor in this case; instead, energy is extracted from glucose by rearranging the molecular structure of the sugar into a more favorable ("low energy") configuration, without any net donation of electrons.



Note: this is how I use the terms, and I believe this is the most common usage in biochemistry today. But I am sure you can find other sources that define them differently. This is rather common in biology and biochemistry, and these terms are very old and fraught with all sorts of historical connotations. But names are not crucial; understanding the biochemical processes is. The important distinction here is that conversion of glucose to lactate does not oxidize the substrate and therefore needs no external electron acceptor; in this way it is fundamentally different from oxidative metabolism.