Sources cite the solid inner core as being composed of iron-nickel composites. Not radioactive.
Isn't everything radioactive when it's hot enough or under enough pressure?

Also, isn't pressure basically heat? Isn't the constant force of gravity going to cause the core to be hotter than its surroundings? It's under the most pressure.

The law of blackbody radiation says that everything radiates energy in the form of photons, merely due to the fact that it is not at a temperature of absolute 0.
Based on some quick googling (in particular https://en.wikipedia.org/wiki/Earth's_energy_budget), the planet is cooling down in terms of radioactive heat loss at a very similar rate to the warming thanks to sunlight. We're in almost perfect balance.

Considering we're in a vacuum, radioactive heat loss is the only way the planet loses heat. Sure there will be microscopic amounts of conduction thanks to the fact space isn't a perfect vacuum, but surely this is comletely negligible considering we're constantly bathed in sunlight.

Convection and conduction will obviously be significant means for the interior of the planet dissipating heat to the atmosphere, but the atmosphere is merely acting as a buffer to limit the radioactive heat loss. A great amount of thermal radiation reflected at the suface will be absorbed by water vapour before it gets to leave the planet.

Is there any way for the atmopshere to return heat to the interior? Surely this is impossible thanks to the fact the interior is hotter and heat always flows from a hot place to a cold place?

Sounds plausible that it contributes. How much energy is added to the Earth's core by tidal heating over time?
I dug around for a while and this was the best I could find...

In addition to the effect of the ocean tides, there is also a tidal acceleration due to flexing of Earth's crust, but this accounts for only about 4% of the total effect when expressed in terms of heat dissipation.
I don't really know how to interpret this though.

Certainly tidal heating is significant though. The slow process of tidal locking that has claimed the moon and will eventually claim the earth is creating heat wherever it causes friction... in the interior, in the oceans. This alone will maintain a certain level of thermal activity within the planet for as long as the process continues.

As for the 3.5billion years of radiocative decay... I haven't got a clue. I have no idea what can decay for so long. Is it not possible that under the immense pressure within the core, nuclear fusion is happening at a very low rate, just enough to keep producing radiation-emitting matter?

We know nuclear fission is happening down there.

http://blogs.scientificamerican.com/...f-earths-heat/

This claims over half our interior heat is the result of nuclear fission.

And Earth is chock full of such radioactive elements—primarily uranium, thorium and potassium. Over the billions of years of Earth's existence, the radioactive isotopes have been splitting, releasing energy as well as these antineutrinos...
They don't seem to have a problem with these elements taking so long to decay.

There seems an abundance of heat sources to keep things active down there, and a distinct lack of means to lose the heat to space.

I'm only really questioning why the atmosphere doesn't get hotter and hotter as it gains energy from the both interior and the sun, while only radiating the equivilent of the solar energy.