Is the Electric and Magnetic field in an EM wave interacting in the same way static E and B fields? Sorry by the title, I don't know how to ask this:
What happens to a charge when some EM wave passes across it?
If we have an EM wave with really low frequency, is this basically the same as having a static E and B field?
That means if we put a magnet or a charge it will be accelerated in the direction of that field?    
 A: A 'test' charge with no other forces acting on it will at any instant have an acceleration proportional to the electric field at that instant, and in the same direction as that field. To be specific, $$\vec {a (t)} = \frac qm\ \vec {E (t)}.$$
For example, if $\vec{E(t)}=\hat x E_0 \cos (\omega t),$ then $$\vec {a (t)} = \hat x E_0 \frac qm \cos (\omega t).$$
We can obtain the velocity and the displacement by successive integrations, not forgetting the arbitrary constants at each stage.
An important case is the effect of an oscillating electric field on a charge that is also acted upon by spring-like restraining forces and by resistive forces. An electron in a material can be modelled in this way. At very low frequencies of applied electric field the electron's displacement at any instant is simply proportional to the electric field strength at that instant. [However at higher frequencies the electron's motion becomes out of phase with the applied electric field, and the amplitude of the electron's motion follows a resonance curve.]
What about magnetic fields?
I'm afraid that it is not the case that "That means if we put a magnet or a charge it will be accelerated in the direction of that field?"
At very low frequencies of magnetic field a magnet will align itself with the field and will therefore turn if the field changes direction smoothly, or flip if the field flips through 180°. The magnet won't move translationally unless the magnetic field is non-uniform.
In a magnetic field a moving charge experiences a force (the magnetic Lorentz force) at right angles to its velocity. Specifically $$\vec F_{mag} =q \vec v \times \vec B,\ \ \ \ \text{so for a varying magnetic field},\ \ \ \ \vec F_{mag}(t) =q \vec v \times \vec B(t).$$
An electromagnetic waves has both varying electric and magnetic fields, so in the last equation, $\vec v$ will depend upon the previous history of both   $\vec E$ and $\vec B,$ making things quite complicated. However, at low frequencies the magnetic Lorentz force is pretty small compared with the electric Lorentz force, $q \vec E,$ and can often be neglected!
