This question might be tricky because the mutation of interest here is inherited from the dad side (paternal) but affects the mitochondria.

That is, the mutation is not a mutation of the mitochondrial DNA; it is of nuclear DNA which affects mitochondrial function and quality. (Mechanism unknown.)

In their explanation, the NBME says, “Mitochondrial diseases are strictly inherited through the mother” but that is incorrect; it would be more correct for them to have said: Mitochondrial DNA mutations are strictly inherited through the mother.

That is, you can have mitochondrial problems that come from your dad. Mitochondrial DNA mutations, on the other hand, come only from mom.

So, the stem describes a “mitochondrial disease” but it is not a mitochondrial disease dervied from a mitochondrial DNA mutation.

Yes, mitochondria are affected but the mutation is in nuclear DNA that governs the maintenance of "healthy mitochondria".

This explains why dad and dad's brother show the same “proximal muscle weakness of the lower extremities”.

GVHD is due to DONOR T lymphocytes recognizing and targeting recipient cells (usually GI, skin, and liver) [diarrhea, maculopapular rash, hepatomegaly, jaundice]. This also means that this is a Type IV hypersensitivity such as contact dermatitis (poison ivy or a nickel allergy) and the PPD test. Sometimes this is taken advantage of (GVHD is usually seen in bone marrow transplants) in the scenario of bone marrow transplants for leukemia patients where we can yield a "graft-versus-tumor" effect.

Vitamin D plays a role in serum calcium and phosphate homeostasis by promoting the intestinal absorption of calcium and phosphate.

Vitamin D deficiency typically leads to: decreased intestinal calcium absorption, hypocalcemia, increased PTH secretion, and increased PTH-mediated bone resorption.