I've had cats for most of my life. The most common ailments in older cats are Diabetes, arthritis, kidney failure and Thyroid disease. Thyroid is easiest to treat. Diabetes requires daily blood sticks and shots, but it's also treatable. Cats with kidney disease deteriorate slowly....eventually they become very thin and vomit a lot, as kidneys shut down. Most humane remedy is to euthanize.
Older cats with dementia cry a lot. They will often stop in their tracks and wail loudly. Older cats drink more water, so have a plentiful supply....they may start 'missing' the litter box and do their business along the perimeter....arthritis is common and your old feline may have trouble walking and getting around. They often can't make it to the litter box in time so they may adopt new, more convenient locations such as a bed or the living room carpet.
Some suggestions: Place one or two extra litter boxes in key locations. It may help to line the perimeters with puppy pads. Adjusting its diet can help too. It is a matter of trial and error until symptoms improve. Generally speaking older cats do better on wet food.
Arm yourself with a lot of patience, keep plenty of puppy pads on hand and find a trustworthy vet.