Does hydrogen exists as a gas, liquid, and solid within Jupiter?
It exists as a gas, liquid and in its very strange metallic form.
Hydrogen definitely exists as a gas on Jupiter - it makes up about 90% of the atmosphere. There is then a sea if liquid hydrogen around 1000km down but then, bizarrely, there is a layer of metallic hydrogen 20,000km down. Here, the hydrogen atoms have lost their electrons so that they exist as protons in a sea of delocalised (away from atoms of origin) electrons. Subsequently, the hydrogen has an extensive magnetic field. However, this is thought to be liquid.
No one is entirely sure about the core of Jupiter, but it is thought it could be rocky with some hydrogen. Perhaps there is solid hydrogen there, but we don't know. It also gets very hot close to the core (due to the metallic hydrogen) so it seems unlikely as hydrogen needs a chilly 14K to freeze.
There's still lots to find out!