Does Earth produce metallic elements in its core? Does Earth produce metallic elements in its core?
 A: The densest elements (metals) in the Earth fall to the center, due to the gravitational force. The densest elements are radioactive, Earths core is radioactive, Uranium-238 is one radioactive species at the center of the earth.
U-238 decays to Thorium via  alpha emission, due to the electric force
$$^{238}_{92}\text U_{146}\to\quad^{234}_{90}\text {Th}^{2-}_{144}+_2^4\text{He}^{2+}_2$$
The Thorium produced is also radioactive and usually decays via beta minus decay, due to the weak force
$$^{234}_{90}\text {Th}_{144}\to\quad^{234m}_{91}\text{Pa}_{143}^++\,^{0}_{-}e^-_0+ \bar\nu_e $$
  The Uranium metal has transmutated to become Thorium metal which further transmutated producing Protactinium. Many further transmutations occur (probabilistically) until the original nucleus reaches a stable Lead-206.
Nuclear transmutation effectively converts a radioactively unstable metal to a less massive metal by ejecting subatomic particles from the  nucleus.

Yes many metals are being produced in nuclear decay cycles, heavier radioactive metals in Earths core are becoming lighter. The metals produced are chemical different, but numerically there is no more metal atoms than were originally.
These decays also produce a lot of heat. This heat keeps the planet hot in the center and also keeps the outer core and mantle liquid. 
A: By metal-production, I think you're mentioning nuclear fusion (like those that take place in hydrogen bombs and core of stars) by which elements can be produced. If you look at the Wiki article I've linked, you can see a quote:

to be about the same temperature as the surface of the Sun - approximately 5700 K 

I don't think such a low (relative to sun) temperature is sufficient enough to fuse the nuclei of elements (not even hydrogen can fuse at such a low temperature) to form new elements. Nuclear fusion requires to about several million (or sometimes a billion) Kelvin temperature.
So roughly, it's NO - our Earth doesn't..! It lacks a few zeros at its heat value...
