What is happening over the 15 minutes it takes a neutron to decay?
Neutron decays into a proton, electron and electron anti-neutrino. Not only electric charge but also (electronic) lepton number has to be conserved (I'm not very sure in this statement). In short: you start and have to finish with 1 matter particle (anti-matter counts as -1).
Mean time $\neq$ half-life. More on wikipedia.
Physically there is no difference between a 14 minutes old neutron and a fresh neutron. Both will eventually decay. If you would observed a neutron for 14 minutes and then started observing another one, the older one would most probably decayed first. If you would started observing two neutrons after 14 minutes, both would decay with same probability. Why? Because neutrons are indistinguishable. You can't tell which is older. Basically, neutrons don't get older with time. Also decay is purely random and doesn't depend on neutron's past.
The opposite is for humans. Of course an 80 years old person will die first with much greater probability then a child. But what can you say about two human beings, if you wouldn't know anything about them?
There is no trigger for decay. Internal nor external. But there are physical reasons for decay, of course. One of them is, that neutrons are slightly heavier than protons and therefore decays to lower energy state ($E=mc^2$). Why are neutrons heavier, I don't know. But there are reasons for that, too. And this is not because $u$ and $d$ quarks have different weight. Quarks mass is only a small part of neutron and proton mass
The quantum mechanical description of the process gives you probabilities for all possible events and the 15 minutes happen to be the mean life time for this process. It's random and you don't have a guarantee for anything, except that the average result will converge against the propability distribution if you let many neutrons decay. There is "no need to talk about something internally happening" in a different way to end up with the two different possibilities of 14 and 15 minutes. And there is nothing really different between the neutron which decays after 14 minutes and the neutron which decays after 15 minutes aprart from the latter decaying 1 minute later.
I think you are misunderstanding what is meant by a half-life. When you start describing quantum mechanics (and nuclear decay is a fundamentally quantum mechanical event) you have to incorporate statistics. A half-life is the amount of time in which, on average, half of a large number of identical specimen will have decayed. When someone says the half-life of a neutron is 10.4 minutes, what they mean is, given any random neutron, if you wait for 10.4 minutes, there is a 50% chance that the neutron will have decayed during that time.