For oldest, please refer to What is the oldest documented Eastern Martial Art that is still practiced? and What is the oldest martial art?. Also see What qualifies a school or business as a legitimate martial arts system?
In general, there is no formal certification or approval process for martial arts. There may be rank systems within an art like karate or judo, but these are not recognized outside their respective organizations. Anyone can basically open a school for martial arts and call it whatever they want, regardless of whether they have any knowledge or skills. In some areas, there may be a local group like a guild that decides who can open schools, but this would be region-specific.
The de facto standard for appraisal and acceptance is fighting, in a venue like mixed martial arts (MMA). If you can beat other people, then others are likely to want to learn from you.
Because there is no certification process, there is no way to quantify what the youngest martial art is. Somewhere in the world, someone has decided that the things they have learned now constitute a new, unique martial art and probably named it after himself. I would wager this happens a lot.