Granted I get that this kid probably didn't exceed the energy output needed to make this plausible, <snip>
Nuclear energy generation isn't something "magical" or especially difficult per sé. What makes it difficult, is the containment you need to prevent radiation from escaping and measures put in place to prevent the reaction from going out of control (something you also need by the way for conventional power sources) and I seriously doubt that he got hold of such pure radioactive materials that a runaway reaction was any danger. Anyway, all you do for the rest is replacing the heat source of burning wood, coal, oil or anything chemical / mechanical with a radioactive source of heat. The rest of the system, whether that be a peltier pad, stirling engine or steam turbine is pretty much the same.
Now, about that "free energy" you mentioned... As I said, there's no such thing. There's only usable/functional/however-you-wanna-name-it energy, i.e. where you gain more energy from the reaction than you expel to mine and collect the materials and to start and monitor the reaction. Wood is an easy example of that. Takes relatively little energy to chop down a tree, and you gain a lot when you burn it in a fireplace.
//GO.SYSIN DD *, DOODAH, DOODAH