The two might be
electricity ("he" in the story) and magnetism ("I")
When they told me to move away, I told I have no charge left.
Similar electric charges repel each other.
On the other hand, magnetic charges (also known as magnetic monopoles) do not exist. $\nabla \cdot \mathbf {B} =0$
When they told me to curl around them, I told them to increase the intensity in the field.
a changing electric field creates a magnetic field around it. The stronger the change (increase), the greater the curl ($\nabla \times$) of the magnetic field: $\nabla \times \mathbf {B} =\mu _{0}\left(\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)$
When I told him to curl, he was big zero.
An electric field has no loopiness (curl is zero) unless there is a changing magnetic field, that is $\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$,
But when he moved away, A spark was created ...
An electric spark is made of electric charge (electrons) jumping an air gap. However, this might be a reference to photons (electromagnetic radiation), whose speed (c) can handily be deduced from these equations, given the proper constants that can me obtained experimentally.
How are the two? What they are doing?
The two are intertwined, and they are demonstrating
Maxwell's equations,
Or alternatively, they might be enacting some other physics experiment, where the curling is physical more than mathematical.