What is the maximum distance over which van der Waals forces act?
There is no strict upper limit you can place on any type of electromagnetic interaction. That being said, van der Waal's forces are due to the formation of instantaneous dipoles which are a result of perturbations of an otherwise spherically symmetric electron density.

The electric field produced by a dipole decays as $1/r^3$. Therefore, it should not be surprising that the interaction between two instantaneous dipoles decays as $1/r^6$. It's actually not completely obvious this should be the case, but it turns out to be true. At very close distances, the van der Waal's forces actually scale as $1/r^7$ due to an effect from quantum electrodynamics, but chemists don't typically worry about this because the effect is negligible in almost all chemical processes.

The actual distance will vary depending on the system, so it's not like one can give actual numbers for the distance. But, for a system like water, the electrostatic force, which decays as $1/r^2$, can be relevant for distances up to, say, 100 angstroms. So, you can try to back out the scale of the van der Waal's interactions from there.

Another way of saying this is that van der Waal's forces can have an important effect on the first solvation shell of a molecule, but they typically do not have a strong effect beyond that distance.