Do all waves superpose on each other? What would happen if two waves with different frequency were to pass through 1 point in space at the same time? Would they interfere at that point in space? Are superposition and interference the same thing?
 A: No.  In general, only linear waves (i.e. only waves described by a linear differential equation.) will superpose (in the usual sense of the word.) By linearity, the sum of two solutions is also a solution.  Besides the common wave equation
$$
\frac{\partial^2 u}{\partial t^2}=v^2 \nabla^2u
$$
the Schrodinger equation is also linear.  The combination of (linear) waves with different frequencies gives rise to beats (accoustic or otherwise).
This does not hold for non-linear waves, since in general the sum of two solutions is NOT a solution to the non-linear wave equation.  A famous example of a non-linear wave equation is the Korteweg-de Vries equation, which will exhibit soliton (or solitary wave) solutions.  In particular, the ``collision'' of two solitons does not result in interference.
Another example of a non-linear wave common in physics is the non-linear Schrodinger equation, which is used for instance in optical fibers.
A: Superposition is just adding the waves together. So if you have waves $w_1(x,t)$ and $w_2(x,t)$ then the superposition of them is just $w(x,t)=w_1(x,t)+w_2(x,t)$
Typically you hear of either constructive or destructive interference with waves of the same frequency where, at a point in space, the superposition is either at a maximum or 0. If they have different frequencies then you would probably get more of a beat frequency equal to the difference in the two individual frequencies.
