You can eat any chicken, regardless of age or sex. Different ages require different cooking techniques. For older birds, the idea is to cook them very slowly in moist conditions. There are several threads on here that cover that. Crock pots, roasting, stews, plenty of different methods. A pressure cooker is the exception to the rule of slow. But get an appropriate recipe for any of these methods. Many of the newer recipes assume you are cooking the 6 to 8 week old chickens you buy at the store. These recipes will not turn out very well with older chickens.
I do different things, but a standard is to use a crockpot. Cut the chicken into pieces. I put it in a crock pot with a quartered onion, chunks of carrot and celery, a few peppercorns, a bay leaf, maybe some garlic and whatever herbs I have handy. Maybe basil, oregano, thyme, parsley, chives, whatever you think would taste good. Cover with water and cook on low for about 6 to 8 hours. With a younger bird you go quicker and with a really old rooster you might need to go a tad longer, but 6 to 8 hours usually works real well. If you go much longer than 8 hours the meat will often cook off the bone. With a slotted spoon take the meat out, then strain the broth, take the fat off the top, and you have excellent chicken broth.
When I butcher a chicken, I save the back, neck, feet, wings, gizzard, and heart strictly for broth. I do it as above but cook it for about 10 hours, maybe a tad longer. The meat does mostly fall off the bone. I strain the broth through a kitchen strainer with four or five layers of cheesecloth to get the bits out, then separate the fat. I usually get about five pints of really good chicken broth. But I also pick the meat out of the remains. Some you will have to pick of the neck or whatever, but some is sort of free floating. This cooked chicken is great in chicken salad, tacos, or in pasta or rice casseroles.
The feet can get pretty dirty. I scald them well in pretty hot water. The toenails slip right off if I grab them and twist and the skin/scales peel off really easily. Instant clean feet.
When I make broth, I do one batch overnight, start another batch the next morning, then do a third batch the next night, straining and picking meat as I go. I cool off the broth in a metal container sitting in ice water then keep it in the fridge until I am ready to can the broth. Then I do the final straining through the cheesecloth and final fat removal, then can it. My pressure canner hold 18 pints and I usually wind up with around 16 pints of fabulous delicious chicken broth, ready to go.
There are plenty of other ways to use old chicken. This is just one of my standard ways. I once got 11 pints of broth and 5 cups of cooked meat off of one mature rooster. Never believe people when they say a chicken is too old to cook. You just have to know how.