Nuclear reactions happening in the Earth are all radioactive decays. These produce heat, and it's in fact the main contribution (I've written another comment here with a bit more detail) but most of it happens in the continental Crust and in the Mantle.

This nuclear process is not generally dependent on pressure, in fact it mainly happens in the external layers of our planet. The distribution of radiogenic heat depends on where the element that may undergo beta-decay are located. If you are curious, the main elements responsible for this on Earth are Uranium, Thorium and Potassium.

Despite there being large uncertainty, geochemical studies show that these element are not much soluable in the liquid core. Radioactive decay contributes to the heat production in the core for 0.2 TW, while the the total amount of heat produced by the core is around 10-15 TW.

EDIT: well, not all nuclear reactions in the earth are decays. A few occurrences of natural fission reactions have been found, where particular conditions, like more abundance of a certain uranium isotope and different amount of oxygen in the atmosphere, made the fission reactions possible. The only few occurrences known happened in the far geological past in Oklo (region of Gabon).

The main heat sources in the core are secular cooling (i.e. losing primordial heat), latent heat due to the ongoing solidification of the inner region, compositional energy (essentially gravitational energy, the lighter elements in the core do not solidify and some fraction of the core solidify these elements rise up to the liquid part) and radioactive decay.

The estimates in Earth's Core (by Cormier et al., nice book) are around 0.3 TW for radioactive decay and a few TW (2 to 6) each for the others.

As an order of magnitude estimation, compositional changes, phase transition and original heat loss contributes equally, while radiogenic heat is only a minor contribution.

The heat balance we measure at the surface has obviously much more than this. We have to take into account the secular cooling of the mantle itself (16 TW), plus the heat production of continents (8TW) and again the mantle (11 TW), which are mainly radiogenic (data here from the Encyclopedia of Solid Earth Geophysics).
Note that every estimate, despite being in line with scientific consensus, is subject to high uncertainties, due to the very difficult nature of these kind of measures/models.

To close going slightly OT, this combination of heat production and heat loss is the driving force of hot spots and plate tectonics. Which means that the cooling dynamics of the earth is responsible for essentially the entirity of what we observe in the solid earth. Earthquakes, volcanic eruptions, tectonic movement, but also interactions with surface geomorphology are all byproducts of a ball of molten rock cooling.

In reality, geochemical studies suggest that radiogenic heat plays a small role in the energy balance of the core. Cooling and phase transition are the main processes.

The part where radioactive decay is the main heat source is the mantle.

The core is molten because it's hot and under high pressure. Essentially, the Earth was very hot and it's cooling down.

In fact, the size of the solid part, i.e. the Inner Core, continuously increases.