The Earth's core is composed of metal (mostly an alloy of iron and nickel), with an inner solid and outer liquid parts. The majority of Earth's layers are solid, even the mantle is solid (plastic) and acts as such, only when observed through long periods of times does it become liquid in characteristic.
With that being said, yes, volcanoes still exist. Volcanoes only occur when there's part of the mantle that's heating up, similar to how two plates meet, and it melts, forming magma. When the magma escapes the underground via a volcanic vent, you can now call it lava.
And some additional info. The Cluster did not cover the entirety of the Earth's core. It wasn't even in the core to begin with. Peridot said that it was only deeply embedded in the mantle. The Cluster's amalgam of a gemstone is small in comparison to the Earth. The problem is that the collective reformed "body" of the Cluster is larger than Earth, which would destroy the planet upon reformation.