Would hydrogen unlike water in a solid state take less space or be more stable? How would a rocket work using a block of melting solid hydrogen instead of liquid hydrogen? Has and could any kind of liquid fuel other than hydrogen been tried this way and what are the problems with this method?
There are some interesting questions in the 'would it be more stable'. If you did actually have a solid core of hydrogen at 14 Kelvin it would actually be very stable since pretty much any Oxidizer you chose to inject including Oxygen would most likely condense out faster than it could react at those very low temperatures (reaction rates decrease with temperature). It would also be freezing the atmosphere into a solid plug at the nozzle end.
All the energy required to freeze the oxidizer and atmosphere would start to melt the Hydrogen
From that point a number of exciting things would potentially happen:
The Hydrogen may leak past the freezing atmosphere at the base of the rocket and explode/ignite around the pad
The pressure may rise to the point the rocket bursts purely on Hydrogen vapor pressure
The pressure may rise to the point the frozen plug blows out and melting hydrogen flows out as liquid and starts to burn in in pools around the pad.
The temperature/pressure may reach the point where the injected oxidizer stops freezing and starts burning with the hydrogen and rocket actually starts producing thrust, hopefully blowing the atmospheric plug (or perhaps a fitted sealing cap) out.
The above happens but the plug holds long enough that the pressure rise melts the previously frozen atmosphere and/or oxidizer to form a BLEVE inside the rocket.
In addition to the above complications the key advantage of a Hybrid rocket is that one of the two compounds used to propel the rocket are room temperature stable while still allowing some degree of throttle control unlike a solid rocket. For this hydrogen system even if you solve the engineering problems to start it, once you stop the oxidizer flow the Hydrogen will continue to melt and either burn in the atmosphere or just produce thrust as a cold gas jet in space so this rocket has no real shutdown method.
There are also some complications around the low structural strength of materials like steel at <20 Kelvin, and what appears to be the low structural strength of frozen hydrogen unless it is well below the melting point potentially allowing it to flow out the nozzle in solidish form under gravity and/or thrust loads.
The density of solid Hydrogen is slightly more than liquid (0.086g/cm3 vs 0.07) but the better solution to take advantage of that might be forming a slurry as noted by JCRM in comments and using it more conventionally.
The density of solid hydrogen is only slightly more than that of liquid. But a lot of extra mass would be necessary to build a container for the solid hydrogen that is suitable for storage of solid hydrogen as well as hybrid combustion chamber with very high temperature and pressure. Liquid hydrogen would be needed for cooling of the nozzle.
Heat flow to the stored solid hydrogen should be so low that losses of hydrogen by liquefaction and vaporization are small. If most of the solid hydrogen goes liquid during storage, operation of the hybrid rocket would be impossible.
So over all no structural weight reduction is possible by using a solid hybrid rocket instead of a conventional liquid hydrogen rocket.
Control of the ratio of oxygen and hydrogen would be difficult during the burn time. A fuel rich mixture may be needed for protection of the combustion chamber and nozzle against oxygen, but to much hydrogen in the mix would be inefficient.