Is there a minimum age to run with the bulls?
Besides the run, is there stuff to do there with a 15 year old boy?
A "Running of the Bulls" or Encierro as we call it, is not some Disney Land ride, it can be quite dangerous and people train all year for these kinds of things, besides it is not allowed for a minor (sub 18) to begin with, though just to watch then yes.
The Fiesta de San Fermín, known outside of the Spain as "The Running of the Bulls" encompasses much more that just the Encierro (the actual running). The week long festival has pyrotechnics and fireworks displays, processions, music/dancing, partying, Giants parades, Jai alai tournaments, and daily afternoon bull fights.
Take a look at their 2019 English language programme:
http://www.sanfermin.com/en/sanfermin-programme/2019-programme/
I doubt any travel Insurance would cover any injury sustained! Why would you want to take the risk?
More generally, I'm not sure the Sanfermines in Pamplona are the best event to bring a 15-year old to. Even though there is something for everyone there, this type of festival attracts a boisterous crowd (same applies to Bayonne, France during their own festival).
Thanks to all for the response and information about the running of the bulls
I don't want to insist you avoid this, everybody must make their own choice, but you may wish to note that most decent people think the "running of the bulls" is very cruel. So you might want to plan an alternative sight if you realise the cruelty is not for you when you get there.
If you go, be aware that hotel prices skyrocket during the festival with people sometimes making reservations a year in advance. The hotel room we paid $105 dollar a night for in May 2017, was going for $500 a night during the festival. When I took my children to a bullfight when they were 10 and 14, they enjoyed it, but not everyone does. I don’t recall any major, must see, sights to see in the city itself although it is nice to walk around. To me, Pamplona, when there is no festival, is only worth a day.
If you are interested in attending this cruel, sadistic and barbaric event I would implore you to visit the following website to ensure you know what happens: https://www.peta.org.uk/living/what-happens-during-the-running-of-the-bulls-in-pamplona/