I do not think that your cat’s age alone is causing the problems you have mentioned. In fact, I have a very large number of patients who, despite being much older than your cat, use their litter box appropriately and do not vomit frequently.
However, your cat’s age (which I consider to be late middle age), combined with the symptoms you describe, makes me worried that she may be suffering from a medical condition. Middle aged and older cats and dogs are more prone to a variety of problems, such as urinary tract infections, kidney disease, thyroid gland disease, and diabetes, that can cause some of the issues you have listed.
Simple blood and urine tests, combined with a thorough veterinary examination, can identify many of the causes of vomiting and inappropriate urination in pets. Many of the conditions I have mentioned are treatable. If not treated, they may cause pain or decreased lifespan, so I recommend that you take your cat to a veterinarian for an evaluation.