Light does not have mass, but photons are Energy, and E=mc², so it has relativistic mass (Uh I think! ... I'm not a physicist), but that mass is relative to its velocity so its not what we technically think of as mass...

Light also has momentum, which is how it is able to move something, however I don't conceptually understand how light has momentum despite lacking mass, as mass is a component of momentum.

I have not answered your question at all!