**Core Concept**
The question is testing the student's knowledge of genetic disorders associated with congenital abnormalities, chronic diarrhea, and recurrent infections. The underlying principle being tested is the association between specific gene mutations and various clinical manifestations.

**Why the Correct Answer is Right**
The patient's symptoms, including chronic diarrhea with elevated stool fat, recurrent severe respiratory tract infections, and a history of meconium ileus, point towards a diagnosis of Cystic Fibrosis (CF). CF is caused by mutations in the CFTR gene, specifically in the cystic fibrosis transmembrane conductance regulator protein. This protein is responsible for regulating the transport of chloride ions across epithelial cell membranes, which is essential for the proper functioning of sweat, mucus, and digestive fluids. Mutations in the CFTR gene lead to thickened secretions and impaired digestion, resulting in the characteristic symptoms of CF.

**Why Each Wrong Option is Incorrect**
**Option A:** While mutations in the GJB2 gene can cause congenital hearing loss, they are not associated with the patient's symptoms of chronic diarrhea and recurrent respiratory infections.

**Option B:** Mutations in the APC gene are associated with Familial Adenomatous Polyposis (FAP), a genetic disorder that increases the risk of colorectal cancer. However, FAP is not characterized by the patient's symptoms of chronic diarrhea and recurrent respiratory infections.

**Option C:** Mutations in the HNF1A gene are associated with Maturity-Onset Diabetes of the Young (MODY), a form of diabetes that typically presents in young adulthood. However, MODY is not characterized by the patient's symptoms of chronic diarrhea and recurrent respiratory infections.

**Clinical Pearl / High-Yield Fact**
Cystic Fibrosis is a classic example of a genetic disorder that affects multiple organ systems, including the respiratory, gastrointestinal, and reproductive systems. The diagnosis of CF is often delayed due to its variable presentation, but a high index of suspicion should be maintained in patients with a history of recurrent respiratory infections, chronic diarrhea, and congenital abnormalities.

**Correct Answer: C. CFTR**