Equivalent circuits in case of equipotential nodes
Since no current flows on RL, are we authorized to replace it with a
  short circuit, or with an open circuit, and then solve the resulting
  circuit?


Yes you can do this on this particular circuit but be careful about expanding that idea; if you did it on an op-amp circuit (because you assumed that the voltage between Vin- and Vin+ was zero i.e. a virtual earth) you would get into a mess.

It's a similar story when using an op-amp (or BJT) as a voltage follower in (for instance), a Sallen Key filter.

In other words you have to be selective to how far you can generally assume that an open circuit can be a short circuit (or vice versa) if the voltages are equal.