1. Your question is not about it. And not even about the law in it. But the ordinary relations of civil nature. The fact that the work is the completion of the website, nothing changes from the point of view of the contractual relationship - it's just a job.
2. To sign a full employment contract with a minor without parental consent impossible
I wouldn't mess with. In the case of any joint it can fly a very expensive and very painful. Because of the early age.