The physical background of the experiment is that inside the metal the electrons can occupy states up till a point. These states are more or less continuous, however the electrons fill these states till an energy, called Fermi level. This energy is lower than the energy of electron in vacuum, so the electron needs an extra energy to jump. If the Fermi energy was not lower than vacuum, the electrons would just leave the metal, and fly away. When PE happens and a photon is absorbed, and it gives enough energy, and electron can jump out.
The important point here is that a single photon gives all the energy to a single electron. In a classical theory, light is just wave, it has no reason to excite a specific electron. Also, if it is continuous wave, electrons could collect enough energy just "waiting longer" if the frequency of light is lower. But PE works this way, because light is quantized: one photon is not the same as two photons with half energy. To jump, the electron needs enough energy from a single photon, because the chance that it is hit by two photons is practically zero, and there may not be empty states along the way and so cannot just add up energy piece by piece.
You don't need monochromatic light. If you use monochromatic light, than all the photons correspond to a given energy, therefore easier to interpret the data, but it is just a practical requirement. If you use normal light, all kind of photos will come, some bellow threshold, some above, so all you see is the mixture of zillion energies.
As I said, this is the whole point. The electron cannot just absorb 3 and a half photons to get enough energy. If you have enough energy from a photon, you see PE, if not, there is no PE. The threshold energy which tells you if the energy is enough.