Not quite.
For photoelectric cells, the current depends on the light intensity. Remember that each photon knocks out one electron.
Work is done by the photon on the electron to knock it off the metal surface. The amount of work required varies (depending on location and how tightly bound the electron is to the metal cations). In this case, the threshold frequency gives the minimum work required (to liberate the least tightly bound electrons).
When a greater frequency is used, more electrons can be liberated as there are more energy available to liberate more tightly bound electrons. However, the least bound electrons still require the minimum work, whilst the higher frequency light provides more photon energy, hence these electrons have the greatest 'residual' kinetic energy. The less bound electrons have more kinetic energy than tighter bound electrons (as tighter bound electrons require more energy to liberate).
When a negative voltage is applied, work is done against electrons to reduce their motion. For electrons with not enough kinetic energy, they get knocked back onto the metal surface, but the more energetic ones can still escape. Since some are knocked back, the current decreases. As you apply more reverse voltage, more electrons get knocked back (because fewer electrons have sufficient energy to escape), hence current decreases. Until the reverse voltage reaches and exceeds the max KE, at this point, not even the most energetic can escape, hence no current flows.
Greater velocity does not necessitate greater current. It's difficult to explain, but the general gist is because distance between electrons is not fixed.