Are non-contact forces conservative forces? Some non-contact forces like gravity, electric force are conservative forces. Is this thing right for all non-contact forces?
 A: Even electric fields can be non-conservative. A conservative field has a zero curl, but the curl of the electric field is given by one of Maxwell's equations:
$$ \nabla \times \mathbf E = - \frac{\partial \mathbf B}{\partial t} $$
If the magnetic field $\mathbf B$ is changing with time then $\partial \mathbf B/\partial t \ne 0$ and the curl of the electric field is non-zero, and that means the electric field is non-conservative.
However gravity is always a conservative field. See for example Can gravity ever be considered a non-conservative force?
A: No. Eddy currents are an example of dissipative, non-conservative forces which are non-contact.  Examples include dropping a magnet through a copper tube, or the example below where a magnet swings on a string and is stopped by the metal plate without touching it.
https://youtu.be/sENgdSF8ppA
A conservative force means it is governed by a potential and is reversible. Meaning the force on an object is determined by its position in space, and by returning to the original position you can recover the energy – eg a pendulum in a gravitational potential field.
