I understand from elsewhere that it is a mistake to think of them as "real" objects but perhaps more as mathematical constructs (If that was a correct understanding) If that is so ,why are they called virtual photons ? Do they "behave" in a photon- like way?
In some mathematical ways, yes, esp. with regard to something called the Green function. I'm not an expert on this but there is a description I find very helpful here, from Matt Strassler: https://profmattstrassler.com/artic...ysics-basics/virtual-particles-what-are-they/ This is all part of the QFT model of matter, according to which physical entities are represented as disturbances in various kinds of fields. But it is not something I studied at university, as it is not needed in chemical physics. There may be others here who can tell you more.
A photon, essentially, is just a quantized package - thus a specific frequency - of energy, that moves at c.
Real photons can, in principle, last forever. The energy of the virtual photon is "borrowed" within the limits of the UP. From the last para of the Electromagnetism section: https://www.britannica.com/science/subatomic-particle/Gravity
Physicists are researching many possibilities...that's what science is all about. So far all we at this time are able to conclude according to the evidence so far, is that "c" is constant and finite.
my physics is not so great, i note you use the term "constant" is that equally applied to things like acceleration and variation ? e.g a range of variations remain constant etc ... i read something a while back saying different light types travel at different speeds. maybe that was not what they meant. maybe it is the observer who measures the light through the gravitational field that perceives the different light at different times while the light is already there ? or speeding around in an arc ? (traveling further yet at the same speed?) (?)... light doesn't change speed, it just goes the longest or shortest way around ?(gravitational-lensing?)
Light travels at a constant speed in a vacuum. It can travel slower though some materials but not faster so that is the point. Nothing can travel faster than that speed. If you travel close to the speed of light and then turn on a light...it still goes the same speed rather than being added to your speed of travel. That is why light's speed is absolute and everything else is relative (time). This is why we have time dilation.