Chronos, be a scientist, just experiment.
Since clay is somewhat heat resistant, there is no special need to fire it after making a mould. Contact with molten metal will kind of fire it anyway.
Remember though that moisture is your enemy. You will have to make sure that the clay is completely dry before you try adding any molten metal. Once it is air dry, you could try putting it in a warm oven for a few hours to make absolutely sure.
Since keys have grooves on both sides, how do you plan to make a three dimensional mould? The MultiPick system appears to use some kind of rubbery substance, so you can plonk the key in vertically while it sets, and then pull the key out without upsetting the mould. You obviously can't do that with clay (or plaster of paris), so you will need a mould in two halves. That is one of your most important challenges to overcome.
For the metal, you could use silver solder, or brazing rod. Ordinary electrical (lead) solder will likely be too soft to make a key, although it is much easier to melt, and might work if you are careful not to be too heavy handed with the result.
Good luck!