Final answer:
The most useful immediate diagnostic test for a patient with advanced AIDS presenting with neurological symptoms is a lumbar puncture for CSF analysis and India ink staining to diagnose potential cryptococcal meningitis.
Step-by-step explanation:
The most useful immediate diagnostic test for a 32-year-old man with HIV presenting with symptoms of mild fever, headache, stiff neck, photophobia, and lethargy, and with a CD4 count of 0 and highly elevated viral load, would be C. Lumbar puncture for CSF analysis and India ink staining. These symptoms and lab findings are suggestive of cryptococcal meningitis, a common opportunistic infection in patients with advanced AIDS. Lumbar puncture with subsequent CSF analysis and India ink staining can help diagnose this condition by identifying the presence of Cryptococcus neoformans, the fungus responsible for the infection.