Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine your partner and obtain a history, I can not tell you what the cause of his symptoms are. However, I will try to provide you with some useful information.
It sounds like he has been sleeping a lot, has tremors, sexual dysfunction. In addition, some vision changes. Depression could be an explanation to all those symptoms (even the tremor, some people under stress can have what is called an enhanced physiologic tremor, or an increase from the very mild tremor most people have sometimes). There are many other causes of tremor, such as essential tremor, which would be most common in his age group, but that condition is not associated wtih excessive sleepiness and the other symptoms you describe.
Parkinson's disease is exceedingly rare at the age of 29, and his symptoms do not fit with this. In addition, MS is more often diagnosed in the context of a definitive focal neurologic deficit such as weakness on one side of the body or the other or numbness, or vision changes with abnormalities seen on eye examination, so this seems less likely though it is still a possibility. MRI of the brain would be needed to definitively exclude MS if there is suspicion for that by his physician.
Certain vitamin deficiencies such as vitamin B12 can cause symptoms that you describe. As you mention, thyroid problems, specifically hypothyroidism, or low thyroid function, can cause such symptoms.
Certain medications or substances such as excessive alcohol intake, and ilicit substances particularly marijuana can lead to these symptoms of apathy and not sleeping too.
In addition, with excessive sleepiness, a sleep disorder such as sleep apnea or other rarer sleep disorders would be a possibility. If he snores and sometimes seems to stop breathing at night, and particularly if he is over weight, sleep apnea would need to be excluded, even at his age.
I recommend continued follow-up with your physician. If other causes of his symptoms are excluded, then treatment of his underlying depression is essential for his well-being, and would also be expected to improve all his other symptoms. Evaluation by a psychiatrist, and sessions with a psychologist in addition to medications will help optimize his treatment.
Thank you for using the forum I hope you find this information useful good luck.