The importance of the cristae comes from the fact that they greatly increase the surface area of the inner membrane of the mitochondria. This is important because this membrane houses the electron transport chain proteins. A larger surface area allows reactions to occur at a higher rate and, thus, more ATP can be generated. The cristae are not essential to protecting the mitochondrial genome or maintaining shape.

The mitochondrion is a double-membraned organelle responsible for generating ATP for the cell. The Krebs cycle is the middle step of cellular respiration, and takes place in the mitochondrial matrix.

While the matrix, outer membrane, and intermembrane spaces are components of mitochondria, the correct answer is inner membrane. The thylakoid space is found in chloroplasts not mitochondria. Compounds are embedded in the inner membrane and transfer electrons from electron donors to electron acceptors by redox reactions. The final enzyme in the chain is ATP synthase, which generates ATP from ADP and inorganic phosphate. 

ATP synthase is the correct enzyme, and it is powered by a  gradient that permits the addition of an inorganic phosphate group to a molecule of ADP. This is located in the inner membrane of the mitochondria, where the ETC is pumping  out to form the necessary gradient required to power ATP synthase. 

The chloroplast has a very simular structure to the mitochondrion, as it is a double-membraned organelle. The chloroplast is used to house the processes of photosynthesis. The light reactions take place in the thylakoid membrane, while the light independent reactions take place in the stroma. 

All three of the given answers are true and supportive of the endosymbiotic theory. Because mitochondria have membranes and genomes similar to those contained by bacteria, it is likely that they were once free-living organisms. The mitochondria have also been known to display remarkable similarities to fossilized microorganisms.

Endosymbiotic theory suggests that mitochondria were once free-living prokaryotes that were engulfed by a larger prokaryote. The engulfed cell still generated a proton gradient between its cell membrane and cell wall for energy synthesis, which the larger surrounding cell was able to use. The larger cell provided protection for the engulfed cell. Over time, the engulfed cell lost some of its distinct features, but continued to produce energy, evolving into the modern mitochondrial organelle.

Ectosymbiosis is a term that refers to an organism that lives on the outside of the host. Both lysosomes and mitochondria are inside of the cell, so these choices cannot be correct.

The endosymbiotic theory postulates that mitochondria were once free-living prokaryotes that have evolved to form a symbiotic relationship with eukaryotic cells. The original prokaryotes were engulfed by larger prokaryotic cells, but continued to generate energy via the membrane gradient. This energy was used by both the smaller engulfed cell and the larger cell, and the smaller cell gained protection and nutrients. Eventually, this relationship evolved into modern eukaryotic cells and mitochondria. There is a plethora of evidence to support this theory. A few examples are that the mitochondrial membranes are more similar in structure to those of bacteria than of eukaryotes, and mitochondria contain their own genomes. 

The endosymbiotic theory states that ancient prokaryotes may have had a symbiotic relationship with early eukaryotes, leading them to become permanent organelles in the eukaryote. Chloroplasts, mitochondria, and flagella have all been tied to this theory. Ribosomes, however, are organelles found in both prokaryotes and eukaryotes, so they are not a part of the theory.

The endosymbotic theory suggests that mitochondria originated from a bacteria that was engulfed by a proto-eukaryotic cell. Much evidence for this theory is based on the fact that mitochondria resemble bacteria in many ways. They do not however contain a peptidoglycan cell wall like almost all bacterial cells do.