Aren't there any rock or similar firm material on/in the gas giant planets? What happens if a rock asteroid hits one of these planets? Shouldn't the rock accumulate in the center of the planet due to its high density?
The inside of a giant planet is not like regular gas.
First of all, it is hot. You are away of how it gets hot inside the Earth (causing volcanos). It is also hot inside Jupiter, but since Jupiter is bigger, it is hotter. It would be hot enough to vaporise rock under "normal conditions".
The pressure is immense, and things stop behaving as you are used to when the pressure is very high. For example, all the atoms in a gas are pushed so close together that they are touching (like they would be in a liquid). This means that there is no boiling point and no real difference between the gas and liquid phases. At extreme pressures, hydrogen atoms are pushed so close together that their electrons can start to flow from atom to atom, forming a fluid metal.
Pressure that can push atoms so close that they can turn hydrogen to a metal mean that you can't send a probe to this region. You can't swim in a metallic hydrogen sea.
Nevertheless, heavier atoms like iron, silicon, carbon, oxygen, will tend to fall towards the centre of the planet, and so there may be a since rocks are made mostly of atoms like iron, silicon, carbon, oxygen, you could describe this as a "rocky" core. But don't think this is a kind of solid surface that you could stand on.