How do we recognize the internal plane of symmetry in meso compounds?
I see two issues here:


Rotational conformations do not change whether or not the molecule is meso. For meso compounds, the presence of the symmetry element means that for each conformation that is chiral, we are guaranteed to have the enatiomeric conformation with equal probability. Therefore, the net optical rotation is zero.
Fischer projections are no doubt a usual way to represent chiral molecules, but in general, we use Fischer projections most heavily in the case of carbohydrates. The reason is because carbohydrates have shared homology where we care about the specific placement of hydroxyl groups. In general, they are not a great visualization tool. Wedge and dashes are much better. In this case, for a simple two carbon system, where the two carbons have identical connectivity, you could just as well have assigned Cahn-Ingold-Prelog absolute stereochemistry to each carbon to see that the molecule is meso.