Question

How does dark matter interact with light?

Answer 1

At this time we don't know what most of dark matter is.  We do know that all dark matter particles are without electrical charge.  Fundamental particles can have a number of intrinsic characteristics.  These include electrical charge, mass, angular momentum and a few other things that we don't sense on human scales.  There's no a priori reason why any particular particle should have any one of these characteristics.  Photons don't seem to have mass, and they don't have electrical charge.  Neutrinos have very little mass and no electrical charge.  The recently discovered Higgs Boson has zero angular momentum.

All our human senses depend on electromagnetic interactions.  This means that we can't directly sense anything, except for light, that has no electrical charge.  Light is the exception because it carries the electromagnetic force or interaction.

It just happens that there is much more mass in things in our universe that have no electrical charge than in things that do or are made of things that have electrical charge.  This is what is meant be dark matter.  It shouldn't be surprising that we didn't discover dark matter until recently, since it doesn't affect any of our senses, and even most of our instruments detect things based on electromagnetic interactions.

The fact that dark matter is indirectly detectable through gravitational effects means that it does have mass and energy.  A small part of it in the form of neutrinos also has angular momentum.  We don't know if the rest of dark matter has angular momentum.

There may even be particles that have no electrical charge or mass, but would they even "matter," since we might not be able to detect them

Answer 2

Dark matter cannot be seen as the are extremely smaller in nature.

➠ they don't stay as a whole and be independent.