What is highest water pressure at which electrolysis can be performed? What is highest water pressure at which electrolysis can be performed to derive hydrogen and oxygen? Does the dielectric constant of water, which which lowers as pressure increases, have an effect on this?
 A: A high-pressure environment tends to favor liquids over gases, insofar as liquids have higher density. So the higher pressure it is, the higher voltage you need to apply to make the reaction H2O --> H2+O2 occur.
But, with a high enough voltage, it should always be possible. ANY electrolytic reaction will eventually occur if you crank up the voltage high enough. Electrolysis only becomes impossible (in practice) (impossible at any voltage), if competing reactions are favored. I'm not sure what the competing reactions would be for electrolyzing pure water in a high-pressure environment. For example, presumably, H2O --> H2 + O3 (ozone gas) would be favored over H2O --> H2 + O2 at high enough pressure.
It's impossible to be quantitative here, because the catalyst and reaction mechanism also make a huge difference to favor one reaction over another. It's not enough to JUST calculate free energies.
A: for each gas there is  the maximum compressibility factor (Q); and since we have two products  hydrogen and oxygen we go by the lowest (Q) which is for oxygen  therefore in case of water electrolysis under high pressure  you expect your reaction to stop when the pressure inside reaches (Q) .
now  to find  (Q). how we do that?  for a gas you need to see how much is its density when it`s liquid ( liter per kg  as example) then the fifth of that should be the maximum density you can get by any given pressure because after that pressure you would cause the atoms to fuse which means potentially  releasing  the Energy MC^2 
