If two waves with equal amplitudes and wavelengths travel through a medium in such a way that a particular particle of the medium is at the crest of one wave and at the trough of the other wave at the same time, what will happen to that particle?

As per the law of superposition we know that when two waves superimpose at a point on the medium then the resultant displacement of the medium particle is vector sum of the displacement due to each wave.

So here by superposition principle we can write

now here we know that one of the wave reaches with crest while other wave reaches at trough position.

So we will have

so here by superposition we will have

so after superposition the medium particle will come to its mean position.

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.