Since my son showed an interest in cooking, he has always helped me out. He has his own apron and whilst he particularly loves making cakes, he also likes helping out with making dinners. I wouldn't be pushing it on a kid that wasn't overly interested, but I would say that under parental supervision kids from the age of 2 or so should be able to help out in the kitchen. In terms of cooking on the stove on their own (with a watchful eye from the parent), I would say that it comes down the skill and confidence of the child as this can vary considerably irrespective of the actual age. I think it is a good life skill that all kids should learn at some stage for when they leave home and need to cook on their own, but also so that they can learn about nutrition and health from a young age.
Depends on if your stove has an open flame or not. If it doesn't, then as long as you are with them supervising, then I think 8 is okay. If it is an open flame, then I would say 11 with supervision. Without supervision I would say 14.
I agree that it's best to start cooking on the stove (supervised) when they're young. It is so important to teach kids to cook for themselves to encourage healthy eating habits rather than relying on junk food. Even small children can help flip a pancake or stir the spaghetti - just get them involved and it will be easier later on.