How does a catalyst accelerate both forward/reverse reactions simultaneously?
The idea is that the activation energies is lowered for both the forward and backward reactions.



Though the activation energy for the backward reaction is higher than the activation energy for the forward reaction, it is nevertheless lowered.

To answer your second question, reactions aren't always reversible, but a lot of the time they are, and are subject to the principle of microscopic reversibility. That means when reactions are performed as a series of steps, at equilibrium, each individual reaction occurs in such a way that the forward and reverse rates of reaction are equal, and these equilibriums can be affected to drive the reaction one way or the other.