I'm not having a go at you, or your article, but when I nitpick something, like to be thorough. Also, I want to build up some credibility by pointing out some things the readers failed to notice, in order that my "pet peeve", which I leave till last, will be given due consideration by the reader.
You wrote, "[E^2 = m^2 * c^4 + p^2 * c^2] This is a fantastic formula. If the system in question is a massless particle then the energy is given by E = ρ c and if it is a system in rest, then the momentum is zero and the equation boils down to the good old E = m c²."
Not your best paragraph, I'm afraid.
First, it's distracting to see gaps where there should be none in E = pc and and E = mc^2.
Second, your "p" is actually the Greek letter rho, not "p" at all., which in physics stands not for momentum but for density.
Third, by saying "and if it is" you seem to say that you are still referring to same system that you stated to be a massless particle which is not your intention at all (correct me if I am wrong about this). It would be better to write "but if it is not massless, and is at rest" because that is clear.
Fourth, the phrase is "at rest" not "in rest".
Fifth, the word "system" doesn't add anything here. Better to say, instead of "If it is a system in rest", "if it is at rest". Also, "if the system is question is a massless particle" is strange to wrong. A system of particles makes sense as an idea, but a single particle is not normally called a system, and I suspect it's illogical to say this. Better to just say, "If we are talking about a massless particle"
Sixth, and this is my pet peeve, if you like (I prefer to think of it as an insight), the word "massless" is liable to be misunderstood/understood to mean "lacking mass in any sense of the word", by many, probably most, laymen, and by many, probably most, people with a bachelors in physics. Most will conclude that the "massless" particle you refer to is therefore weightless, and does not contribute to the mass of any system it is part of. Some intelligent laymen will conclude that without mass, there can be no momentum, since momentum is mass times velocity as every school kid knows, and be mightily confused to see you saying that the "massless particle" has momentum. Much better to say, at least in an article clearly aimed at laymen like this one, but maybe even in one aimed at particle physicists, "a particle with no rest mass". One *could* go further and speak of "a 'restmassless' particle". I coined the word "restmassless" and also "restmasslessness" and "restmass". I hope (perhaps fondly) that the latter word will become used so much that it starts be as as easy to pronounce as "Christmas" ("KRISSmuss" and "RESSmuss", respectively). Endless confusion is caused by the use of the word "mass" unqualified in the context of relativity. Millions of people think that energy cannot contribute the mass of the object it is in, because they know that photon is pure energy and have heard that the photon is massless. The other day, a great expert in physics, who I won't name, said that the weight of an object as measured by a weighing scales at rest is the same regardless of whether the object is sliding horizontally on the scales (moving with respect to the scales). I had just said that the weight is different, while the rest mass is the same, and he thought he was correcting me. It shows that even real physicists can be confused about this. I think the reason he got confused was in part because he used the term "mass" alone, and never "rest mass".