I would never suggest homeopathic remedies before a diagnosis is made by a competent professional.
With these symptoms, I STRONGLY recommend that the owner take this cat to a veterinarian. It is very important to get a diagnosis first before you speculate on any treatment. Bloodwork and xrays may be required. This kitty is obviously quite sick and the sooner he goes, the better he will do.
I don't believe that his condition is from the lack of litter changing. At thirteen years of age, he is a senior citizen and metabolic diseases are quite common.
Good luck. If he is as sweet and terrific as you say he is, he deserves the very best of care!