Supercapacitor and an applied exterior magnetic field?
If the Supercap is placed inside an area where an exterior magnetic
  field Bext is applied, while the capacitor is charged, and connected
  to a load, would the +/- ions move quicker(since the electrostatic
  force would push like charges away + the Lorentz force) from the
  double layer towards the electrolyte?


Notice that the Lorentz force is perpendicular to both the magnetic field and the direction of the charges' movement. So, will charges travelling through the magnetic field experience Lorentz force? - Yes, but only one perpendicular to their own motion, so charging/discharging rate is not increased by a static magnetic field (otherwise, you'd be violating §1 of thermodynamics). It might even decrease a little because the electrons may have to travel further because they are deflected from the shortest path.

Many capacitors (from electrolyte to "Ultra-Caps") are made by spooling sheets of electrode materials around a center rod, which means that the Lorentz forces in most directions will cancel each other out almost completely. (The electrons travel along the spool on almost circular paths experiencing a Lorentz force in one direction on one half of a circle and a force in the opposite direction on the other half.)