Do stars have metal and rocky cores?

If it were to have a rocky core, it would be unable to start fusion, and wouldn't be a star. As for why it's not solid, the sheer pressure of the mass of the star keeps the core in a plasma-gaseous state. The heat ensures that it will never be solid. Even the rocky planets don't have solid cores, not completely. read more

The planetary core consists of the innermost layer(s) of a planet; which may be composed of solid and liquid layers. Cores of specific planets may be entirely solid or entirely liquid. In the Solar System, core size can range from about 20% to 85% of a planet's radius . read more